online_dimensionless_uh_cascade:   Dimensionless unit hydrograph by the cascade of linear reservoirs 


C = tr/K          C1 = C/(2+C)           C2 = (2-C)/(2+C)

Qj+1n+1 = 2C1(Qaverage)j + C2Qj+1n



Fon a chosen Courant number C and number of linear reservoirs N, there is a unique dimensionless unit hydrograph based on the cascade of linear reservoirs. The dimensionless unit hydrograph has dimensionless time t* as abscissa and dimensionless discharge Q* as ordinate.

The dimensionless time is t* = t / tr, in which tr is the duration of the unit hydrograph, in hours.

The dimensionless discharge is Q* = Q / Qm, in which Qm = 2.777778 (A / tr), is the maximum attainable discharge (runoff concentration only), in m3/s. In this formula, basin area A is in km2; unit hydrograph duration tr is in hours.

The dimensionless unit hydrograph is independent of unit hydrograph duration tr and reservoir storage constant K, and is dependent only on their ratio C = tr / K. The dimensionless unit hydrograph is independent of the basin area A.

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