Effects of sea level rise on the salinity of Bahmanshir estuary

Abstract

Bahmanshir estuary, which is connected to the Persian Gulf, is one of the most important water resources in region. In this study, saltwater intrusion due to possible sea level rise in the Bahmanshir estuary was investigated. A one-dimensional hydrodynamic and water quality model was used for the simulation of the salinity intrusion and associated water quality, with measured field data being used for model calibration and verification. The verified model was then used as a virtual laboratory to study the effects of different parameters on the salinity intrusion. A coupled gas-cycle/climate model was used to generate the climate change scenarios in the studied area that showed sea level rises varying from 30 to 90 cm for 2100. The models were then combined to assess the impact of future sea level rise on the salinity distribution in the Bahmanshir estuary. Using important dimensionless numbers, a dimensionally homogenous equation was subsequently developed for the prediction of the salinity intrusion length, showing that the salinity intrusion length is inversely correlated with the discharge and directly with the sea level rise. In addition, the magnitude and frequency of the salinity standard violations at the pump station were predicted for 2100, showing that the salinity violations under climate change effects can increase to 45 % of the times at this location. This reveals the importance of this type of approach for considering future infrastructure management.

Appendix

Numerical discretization of the governing equations.

Conservation of mass:

$$\frac{\partial Q}{\partial x} + b_{\text{s}} \frac{\partial h}{\partial t} = q$$

(10)

where b _s is the storage width

The derivatives of Eq. 10 can be shown as

$$\frac{\partial Q}{\partial x} \approx \frac{{\frac{{\left( {Q_{j + 1}^{n + 1} + Q_{j + 1}^{n} } \right)}}{2} - \frac{{\left( {Q_{j - 1}^{n + 1} + Q_{j - 1}^{n} } \right)}}{2}}}{{\Delta 2x_{j} }}$$

(11)

$$\frac{\partial h}{\partial t} \approx \frac{{\left( {h_{j}^{n + 1} - h_{j}^{n} } \right)}}{{\Delta t}}$$

(12)

b _s in Eq. 10 can be approximated as

$$b_{\text{s}} = \frac{{A_{j} + A_{j + 1} }}{{\Delta 2x_{j} }}$$

(13)

Inserting the derivatives in Eq. 10 yields

$$\alpha_{j} Q_{j - 1}^{n + 1} + \beta_{j} h_{j}^{n + 1} + \gamma_{j} Q_{j + 1}^{n + 1} = \delta_{j}$$

(14)

Momentum conservation equation:

$$\frac{\partial Q}{\partial t} \approx \frac{{Q_{j}^{n + 1} - Q_{j}^{n} }}{{\Delta t}}$$

(15)

$$\frac{{\partial \left( {\alpha \frac{{Q^{2} }}{A}} \right)}}{\partial x} \approx \frac{{\left[ {\alpha \frac{{Q^{2} }}{A}} \right]_{j + 1}^{{n + {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}} - \left[ {\alpha \frac{{Q^{2} }}{A}} \right]_{j - 1}^{{n + {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}} }}{{\Delta 2x_{j} }}$$

(16)

$$\frac{\partial h}{\partial x} \approx \frac{{\frac{{\left( {h_{j + 1}^{n + 1} + h_{j + 1}^{n} } \right)}}{2} - \frac{{\left( {h_{j - 1}^{n + 1} + h_{j - 1}^{n} } \right)}}{2}}}{{\Delta 2x_{j} }}$$

(17)

Inserting these derivatives’ in the conservation of momentum equation yields

$$\alpha_{j} h_{j - 1}^{n + 1} + \beta_{j} Q_{j}^{n + 1} + \gamma_{j} h_{j + 1}^{n + 1} = \delta_{j}$$

(18)

where

$$\alpha_{j} = f\left( A \right)$$

(19)

$$\beta_{j} = f\left( {Q_{j}^{n} ,\Delta t,\Delta x,C,A,R} \right)$$

(20)

$$\gamma_{j} = f\left( A \right)$$

(21)

$$\delta_{j} = f\left( {A,\Delta x,\Delta t,\alpha ,q,v,\theta ,h_{j - 1}^{n} ,Q_{j - 1}^{{n + {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}} ,Q_{j}^{n} ,h_{j + 1}^{n} ,Q_{j + 1}^{{n + {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}} } \right)$$

(22)

Therefore, the momentum and mass conservation equations can be written in a similar form as follows

$$\alpha_{j} Z_{j - 1}^{n + 1} + \beta_{j} Z_{j}^{n + 1} + \gamma_{j} Z_{j + 1}^{n + 1} = \delta_{j}$$

(23)