Hydrodynamic and Total Dissolved Solids Model of the Tigris River Using CE-QUAL-W2

Abstract

The headwaters of the Tigris River basin in Iraq is controlled by Turkey due to a series of dams constructed over the last few decades. Since Total Dissolved Solids (TDS) in the Tigris River within Baghdad and downstream cities can reach 1000 mg/L exceeding both drinking water and irrigation guidelines, a hydrodynamic and water quality model, CE-QUAL-W2, of the river was developed to understand how changes in flow affect TDS downstream. A model of 880 km of the Tigris River from Mosul Dam to Kut Barrage including Tharthar Lake was constructed for 2009. Model development was challenging due to a lack of in-situ measurements for calibration. Comparison of flow measurements and model predictions at downstream locations agreed well with field measurements, with model flow errors generally less than 2%. We evaluated the effect of changing upstream flow conditions on total dissolved solids concentrations in the Tigris River in order to see how headwater flow control affects TDS. A sensitivity study suggested that increasing upstream river flow by 15% results in about a 5% decrease in TDS concentration. It was recommended to maintain an average annual flow in the Tigris River within Baghdad above 420 m³/s to keep total dissolved solids concentration below 500 mg/L and to strictly control flows through Tharthar Lake and irrigation return flows into the mainstem of the Tigris River.

Appendix A CE-QUAL-W2 Governing Equations

The water quality state variables include (Cole and Wells 2017):

• 1. any number of generic constituents defined by a 0 and/or a 1st order decay rate and/or a settling velocity and/or an Arrhenius temperature rate multiplier that can be used to define any number of the following:

  • a. conservative tracer(s)

  • b. water age or hydraulic residence time

  • c. N₂ gas and %Total Dissolved Gas

  • d. coliform bacteria(s)

  • e. contaminant(s)

• 2. any number of inorganic suspended solids groups

• 3. any number of phytoplankton groups

• 4. any number of periphyton/epiphyton groups

• 5. any number of CBOD groups

• 6. any number of submerged macrophyte groups

• 7. ammonium

• 8. nitrate+nitrite

• 9. bioavailable phosphorus (commonly represented by orthophosphate or soluble reactive phosphorus)

• 10. silica (dissolved and particulate)

• 11. labile dissolved organic matter

• 12. refractory dissolved organic matter

• 13. labile particulate organic matter

• 14. refractory particulate organic matter

• 15. total inorganic carbon

• 16. alkalinity

• 17. iron and manganese

• 18. dissolved oxygen

• 19. organic sediments

• 20. gas entrainment

• 21. any number of macrophyte groups

• 22. any number of zooplankton groups

• 23. labile dissolved organic matter-P

• 24. refractory dissolved organic matter-P

• 25. labile particulate organic matter-P

• 26. refractory particulate organic matter-P

• 27. labile dissolved organic matter-N

• 28. refractory dissolved organic matter-N

• 29. labile particulate organic matter-N

• 30. refractory particulate organic matter-N

• 31. Sediment and water column CH₄

• 32. Sediment and water column H₂S

• 33. Sediment and water column SO₄

• 34. Sediment and water column Sulfide

• 35. Sediment and water column FeOOH(s)

• 36. Sediment and water column Fe⁺²

• 37. Sediment and water column MnO₂(s)

• 38. Sediment and water column Mn⁺²

• 39. Sediment organic P, sediment PO₄

• 40. Sediment organic N, sediment NO₃, sediment NH₄

• 41. Sediment Temperature

• 42. Sediment pH

• 43. Sediment alkalinity

• 44. Sediment Total inorganic C

• 45. Sediment organic C

• 46. Turbidity correlation to Suspended solids

1.1 Governing Eqs

X-Momentum

$$ \frac{\partial UB}{\partial t}+\frac{\partial UUB}{\partial x}+\frac{\partial WUB}{\partial z}=-\frac{1}{\rho}\frac{\partial BP}{\partial x}+\frac{\partial \left(B{A}_x\frac{\partial U}{\partial x}\right)}{\partial x}+\frac{\partial B{\tau}_x}{\partial z} $$

Where

U:

Longitudinal, laterally averaged velocity, m/s

B:

Water body width, m

t:

Time, s

x:

Longitudinal Cartesian coordinate

z:

Vertical Cartesian coordinate

W:

Vertical, laterally averaged velocity, m/s

ρ:

Density, kg/m³

P:

Pressure, N/m²

A_x:

Longitudinal momentum dispersion coefficient, m²/s²

τ_x:

Shear stress per unit mass, m²/s²

Z-Momentum

$$ 0=g-\frac{1}{\rho}\frac{\partial P}{\partial z} $$

Where

g:

acceleration due to gravity, m/s2

Continuity

$$ \frac{\partial UB}{\partial x}+\frac{\partial WB}{\partial z}= qB $$

Where

q:

lateral boundary inflow or outflow, m3/s

Free-Surface

$$ \frac{\partial {B}_{\eta}\eta }{\partial t}=\frac{\partial }{\partial x}{\int}_{\eta}^h UBdz-{\int}_{\eta}^h qBdz $$

Where

B_η:

Spatially and temporally varying surface width, m

η:

Free water surface location, m

h:

Total depth, m

Constituent Transport

$$ \frac{\partial B\varphi}{\partial t}+\frac{\partial UB\varphi}{\partial x}+\frac{\partial WB\varphi}{\partial z}-\frac{\partial \left(B{D}_x\frac{\partial \varphi }{\partial x}\right)}{\partial x}-\frac{\partial \left(B{D}_z\frac{\partial \varphi }{\partial z}\right)}{\partial z}={q}_{\varphi }B+{S}_kB $$

Where

φ:

Laterally averaged constituent concentration, mg/L

D_x:

Longitudinal temperature and constituent dispersion coefficient, m²/s

D_z:

Vertical temperature and constituent dispersion coefficient, m²/s

q_φ:

Lateral inflow or outflow mass flow rate of constituent per unit volume, mg/L/s

S_k:

Kinetics source/sink term for constituent

Equation of State

$$ \rho =f\left(T,{\varphi}_{TDS},{\varphi}_{SS}\right) $$

Where

T:

Temperature, ^oC

φ_TDS:

Total dissolved solids concentration, mg/L

φ_SS:

Suspended solids concentration, mg/L