Contribution of strontium to the study of groundwater salinity. Case of the alluvial plain of Sidi Bel Abbes (Northwestern Algeria)

Abstract

Strontium contents are an indispensable complement to the measures of chlorides, sodium and sulfates to explain the anomalies of groundwater salinity. This approach of natural tracers is applied to Sidi Bel Abbes plain to study the processes of salinization of the aquifer. Chemical analyses performed on 68 wells capturing the unconfined aquifer of the Sidi Bel Abbes plain reveal a correspondence in spatial evolution of chemical elements. Their concentration and their distribution in the plain argue for the presence of evaporite deposits, until now unknown in the Plio-Quaternary detrital sediment filling. This evaporitic sedimentation is more present on the northern edge of the plain where the detrital deposits are of mixed origin: Tellian and meridional. Tellian sediments represented mainly by marls interspersed with Triassic formations are mixed with carbonatic stream sediment coming from the south, and this mixture provides an environment rich in sulfates and carbonates. The geographic and climatic conditions will allow the precipitation of evaporite minerals and diagenetic replacements: gypsum, anhydrite, halite and celestine. These formations not visible in outcrop leave their imprint in groundwater. This study enabled us to learn about the lithological nature of detrital and evaporite sediments of Sidi Bel Abbes plain as well as the diagenetic stages of evaporite minerals formed during the Pliocene period in the north of the plain. The solubility and the dissolution of evaporite deposits present in the Plio-Quaternary detrital filling is the principal process that controls water salinity of the Sidi Bel Abbes plain.

Appendix

The structural parameters of the semi-variogram describing the model are:

• 1. The nugget variance which is the intercept of the semi-variogram model representing the variation of the studied variables; the smoothing of the grid will depend on the nugget effect, the larger it is, the more smoothing is important.

• 2. The sill indicating that the asymptote of the curve where the structural variance reaches its maximum value, because it remains constant.

• 3. The range that indicates the distance value at which the variance of the variables is reached, which defines the area of influence of autocorrelation.

The theoretical variogram chosen for modeling was a mixture of nugget and spherical models (Journel and Huijbregts 1978; Sanchèz-Marthos et al. 2001).

$${\text{Nugget}} \quad \gamma (h) = \left\{ {\begin{array}{*{20}l} 0 \hfill & {{\text{if}}\;h = 0} \hfill \\ {c_{1} ,c_{2}{:}\;{\text{constant}}} \hfill & {{\text{if}}\;h > 0} \hfill \\ \end{array} } \right\} \Rightarrow c\; {\text{Nug}}$$

$${\text{Spherical}}\quad \gamma \left( h \right) = \begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}l} {c_{2} \left[ {1.5\frac{h}{a} - 0.5 \, \left( {\frac{h}{a}} \right)^{3} } \right]} \hfill & {{\text{if}}\;0 \le h \le a} \hfill \\ {c_{2} } \hfill & {{\text{if}}\;h > \, a} \hfill \\ \end{array} } \right\} \Rightarrow c \, \;{\text{Sph}}\left( a \right)} \\ {a, \, c_{2} {:}\;{\text{constant}}} \\ \end{array}$$

a = range, c = sill.

Cross-validation

The formulas used for cross-validation are as follows:

The mean error is the averaged difference between the measured and the predicted values, it is calculated from:

$${\text{M}} . {\text{E}} = \frac{{\sum\nolimits_{i = 1}^{n} {\left( {\hat{z}(x_{i} ) - z(x_{i} )} \right)} }}{n}$$

where, n is the number of samples; $\hat{z}(x_{i} )$ is the estimate and z(x _i ) is the measured value.

The root-mean-square error indicates how closely the model predicts the measured values. The smallest value is better.

$${\text{R}} . {\text{M}} . {\text{S}} . {\text{E}} = \sqrt {\frac{{\sum\nolimits_{i = 1}^{n} {\left( {\hat{z}(x_{i} ) - z(x_{i} )} \right)}^{2} }}{n}} .$$

The root-mean-square standardized error is calculated from: ${\text{S}} . {\text{R}} . {\text{M}} . {\text{S}} . {\text{E}} = \sqrt {\frac{{\sum\nolimits_{i = 1}^{n} {\left[ {{{\left( {\hat{z}(x_{i} ) - z(x_{i} )} \right)} \mathord{\left/ {\vphantom {{\left( {\hat{z}(x_{i} ) - z(x_{i} )} \right)} {\hat{\sigma }(x_{i} )}}} \right. \kern-0pt} {\hat{\sigma }(x_{i} )}}} \right]^{2} } }}{n}}$where $[\hat{\sigma }(x_{i} )]^{2}$ is the predicted standard error, n: number of samples, $\hat{z}(x_{i} )$: predicted value, z(x _i ): measured value.