Runoff Model (reservoir) - Non-linear Reservoir

Non-linear Reservoir

Contrary to the linear reservoir, the non linear reservoir has a reaction factor A that is not a constant, but it is a function of S or Q (figure 2, 3).

Normally A increases with Q and S because the higher the water level is the higher the discharge capacity becomes. The factor is therefore called Aq instead of A.
The non-linear reservoir has no usable unit hydrograph.

During periods without rainfall or recharge, i.e. when R = 0, the runoff equation reduces to

• Q2 = Q1 exp { − Aq (T2 − T1) }, or:

or, using a unit time step (T2 − T1 = 1) and solving for Aq:

• Aq = − ln (Q2/Q1)

Hence, the reaction or response factor Aq can be determined from runoff or discharge measurements using unit time steps during dry spells, employing a numerical method.

Figure 3 shows the relation between Aq (Alpha) and Q for a small valley (Rogbom) in Sierra Leone.
Figure 4 shows observed and simulated or reconstructed discharge hydrograph of the watercourse at the downstream end of the same valley.