Flow Routing & Hydrologic Routing

• Flow routing involves determining the flow hydrograph at a point on a watershed using a known upstream hydrograph.
• It helps predict the shape of a hydrograph in channels, reservoirs, or lakes.
• Routing provides timing and magnitude of flow downstream.
• The effect of measured or estimated discharge is observed at other locations, often upstream.
• The terms flow and discharge are often used interchangeably.
• Routing allows estimation of downstream river levels, or upstream levels in tidal zones.
• When a hydrograph travels, it attenuates and gets delayed.
• Storage is the difference between inflow and outflow.
• Peak discharge is lower at the downstream end; thus, inflow peak is greater than outflow peak.
• Attenuation can be determined by the formula: %Attenuation = ((Ip - Qp) / Ip) * 100%
• Time to peak becomes larger downstream due to lag and attenuation.
• Assuming no losses from seepage, volume remains the same at the downstream end.

Hydrologic Routing

• In hydrologic routing, flow is calculated as a function of just time at a specified location.
• Governed by continuity, and flow/storage relationships.
• It is considered a simple approach.

Hydraulic Routing

• Flow is calculated as a function of both space and time throughout the system.
• Governed by continuity and momentum equations, and solves partial differential equations of open channel flow.

Hydrologic Routing Method

• Input, output, and storage are related by the continuity equation: dS/dt = I(t) - Q(t)
• Q and S are unknown.
• Storage can be expressed as a function of inflow I(t), outflow Q(t), or both: S = f(I, dI/dt,...,Q, dQ/dt,...)
• The approach assumes a relationship between storage and flow to determine flows.

Reservoir vs Channel Routing

• Level Pool method is used for Reservoirs.
• Muskingum method used for River/ Channel routing.

Level Pool Routing Equations

• S(j+1) - S(j) / Δt = I(j) + I(j+1) / 2 - Q(j) + Q(j+1) / 2
• (2S(j+1) / Δt+ Q(j+1)) = (I(j) + I(j+1)) + (2S(j) / Δt - Q(j))
• Where: Delta t is the time step, j is the initial time, j+1 is the time j+delta t, S is storage, I is inflow, and Q is outflow.

Storage-Indication Curve (SIC)

• Outlines procedures to generate outflow hydrograph Q(t) from a reservoir.

Procedure to calculate outflow hydrograph Q(t)

• Estimate inflow hydrograph, I(t)
• Establish outlet stage-discharge relationship (h vs Q)
• Establish basin stage-storage relationship (h vs S)
• Establish discharge-storage relationship (Q vs S) and Q vs ([2S/Δt] + Q)

Calculating Outflow hydrograph Q

• Find I(j) + I(j+1)
• 2S(j) / Δt - Q(j)
• Add (I(j) + I(j+1))
• 2S(j) / Δt - Q(j) to find (2S(j+1) / Δt + Q(j+1))
• Find (2S(j+1) / Δt - Q(j+1)) by subtracting 2Q(j+1) from (2S(j+1) / ∆t + Q(j+1))
• Use the (2S / Δt + Q) vs Q relation to find the corresponding Q(j+1)
• The (2S / Δt + Q) vs Q relationship is dependent on Δt therefore for different Δt’s the relationship must be reconstructed.