Effect of reservoir models and climate change on flood analysis in arid regions

Abstract

Dams are built in arid regions across watersheds for flood control among other purposes. Capacity-elevation (C-E) curves are vital for reservoir routing and dam operation. Different models are available for representing C-E relationships. Power and logarithmic laws are evaluated and tested for reservoir routing. The evaluation is based on the analysis of 136 reservoirs across different regions of Saudi Arabia (SA). The analysis revealed that 75.7% of the reservoirs are of flood plain foothill type. A case study on Al-Lith dam basin is utilized for application based on measured events. The resulting routed outflow hydrographs showed that the logarithmic law is better to represent the reservoir than the power law. With respect to the climate change effect, the results show that the predicted rainfall from Representative Concentration Pathways scenario (RCP4.5) increased by about 20 to 31.4% from 5 to 100 years return periods respectively with an average of 27%. While for scenario RCP8.5, the predicted rainfall increased by 42% to about 55% from 5 to 100 years return periods respectively with an average of 49%. For the RCP4.5 scenario, the peak flows, Q_p, and volumes, W, increased by an average of 69% and 67% respectively. While for the RCP8.5 scenario, the same parameters increased by an average of 139% and 134% respectively. The effect of transmission losses in the results seems to be minor with respect to climate change signal (for RCP4.5, Q_p and W are lowered on average by 2% and 0.5% respectively, and for RCP8.5, Q_p and W are lowered on average by 4.5% and 1.3% respectively). The results of this research recommend to use the logarithmic law and to take into account the effect of climate change on future dam projects in SA.

Appendix

The mass conservation equation for reservoir routing is given by the following:

$$ \frac{dW(t)}{dt}=I(t)-O(t), $$

(18)

where W(t) is the storage of the reservoir, I(t) is the inflow hydrograph upstream the dam, and O(t) is the outflow hydrograph downstream the dam passed over the spillway.

The spillway equation reads as follows:

$$ O(t)= CB{\left[Z\hbox{--} P\right]}^{1.5}\kern0.5em \mathrm{if}\ Z>P $$

(19)

$$ O(t)=0\kern5em \mathrm{if}\ Z\le P $$

(20)

where C is the discharge coefficient, B is the spillway width, Z is water depth measured from the reservoir bottom, and P is the spillway height measured from the reservoir bottom.

The storage term in Eq. (18) is required to be assessed. This term can be rewritten as follows:

$$ \kern5.25em \frac{dW(t)}{dt}=\frac{dW(t)}{dZ}\frac{dZ}{dt}=A(Z)\frac{dZ}{dt} $$

(21)

where A(Z) is the surface area of the reservoir. Substituting Eq. (21) in Eq. (18) yields the following:

$$ \frac{dZ}{dt}=\frac{I(t)-O(t)}{A(Z)} $$

(22)

The two methods presented earlier (the power law and the logarithmic law) are used to quantify the surface area of the reservoir by differentiating Eqs. (1) and (2). Then substituting in Eq. (22) including Eqs. (19) and (20) for the reservoir outlet yields the following equations for the power law and the logarithmic law respectively presented in the paper  (Eqs. 8 and 9).