LIN_RES_STORt1 = LIN_RES_STORt 0 + dt(INFLOW_5∆t - OUTFLOW_5∆t )
(46)
where
INFLOW_5 = SURF1+SURF2+SURF3+SURF4+SURF5
(47)
OUTFLOW_5 = LIN_RES_STOR / KL
(48)
In eq 46, LIN_RES_STOR (the equivalent of dS/dt in eq 38) is incremented by INFLOW_5 (the
equivalent of "I" in eq 46) and decremented by OUTFLOW_5 (the equivalent of the second part of
eq 39). INFLOW_5 contains the sum of the surface runoff from the entire watershed (eq 47). The
outflow from LIN_RES_STOR is delayed within OUTFLOW_5 because OUTFLOW_5 decrements
LIN_RES_STOR by the quotient of LIN_RES_STOR and KL rather than the full amount in
LIN_RES_STOR (eq 48).
Equations 4954 perform the lag and route calculations. The lag and route method is equivalent to
a linear reservoir with an extra delay. Equations 4951 represent the linear reservoir while eq 52
represents the extra delay.
LG_RT_STORt1 = LG_RT_STORt 0 + dt(INFLOW_2∆t - OUTFLOW_2∆t )
(49)
INFLOW_2 = OUTFLOW_5
(50)
OUTFLOW_2 = LG_RT_STOR/KOa
(51)
OUTFLOW_2_LAG = OUTFLOW _ 2t1 TLO
(52)
where TLO is a specified time in hours (see Table 14). The units of surface runoff are converted from
mm/h to m3/s in equation 53.
SRF_RUNOFF = 0.2778 DA OUTFL_2_LAG.
(53)
The total surface runoff from the watershed is calculated by eq 54:
RSUMt1 = RSUMt 0 + dt(SRF_RUNOFF∆t ) .
(54)
In eq 49, LG_RT_STOR is incremented by INFLOW_2 and decremented by OUTFLOW_2
where INFLOW_2 contains the value of OUTFLOW_5 from eq 48. The outflow from
LG_RT_STOR is also delayed because OUTFLOW_2 is the quotient of LG_RT_STOR and KOa
(eq 51). An extra delay is computed in OUTFL_2_LAG as OUTFLOW 2 is delayed in
OUTFL_2_LAG by the value of TLO (eq 52).
In eq 53, the lagged and routed surface runoff is converted from mm/h to m3/s in SRF_RUNOFF
by multiplying OUTFL_2_LAG by DA and 0.2778. Finally, in eq 54, RSUM is incremented by
SRF_RUNOFF to calculate the total amount of surface runoff from the watershed.
Figure 22 shows that flow was lagged by the linear reservoir in the top of Figure 21 because the
peak of INFLOW_5 occurs shortly after 60 hours while the peak for OUTFLOW_5 occurs at rough-
ly 75 hours. Figure 22 also shows the smoothing effect of a linear reservoir because the shape of
OUTFLOW_5 is much smoother than the shape of INFLOW_5. The smoothing is due to delayed
outflow from and storage within the linear reservoir. The difference in magnitude between the peak
of INFLOW_5 and OUTFLOW_5 is also due to the storage effect in the linear reservoir structure.
Figure 23 shows the delays created by the lag and route structure. INFLOW_2 (also equal to
OUTFLOW_5 from the linear reservoir structure) is the input to the lag and route structure and
should therefore peak the earliest. OUTFLOW_2 represents the first delay created by the lag and
route structure and should therefore peak after INFLOW_2. OUTFLOW_2_LAG represents the sec
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