I O = dS/dt
(38)
S=KO
O = S/K.
hence,
(39)
Equation 38 states that the change in storage in a linear reservoir over time (dS/dt) is equal to the
inflow to the linear reservoir (I) minus the outflow from the linear reservior (O). Equation 39 says
that the storage in a linear reservoir (S) is equal to the outflow from the linear reservoir multiplied by
a linear reservoir lag coeffiecient (K). Furthermore, both sides of eq 39 can be divided by K to
calculate the outflow from the linear reservoir (the second part of eq 39).
Equations 4045 are the equations in SBS_STOR_&_FLOW_1. INFLOW_11, SBS_STOR and
OUTFLOW_II from eq 40 are equivalent to I, S and O respectively from eq 38. INFLOW_II is
calculated with eq 41 and 42. OUTFLOW_II in eq 43 is equivalent to O in the second part of eq 39.
INIT_SBS_STOR in eq 44 is equivalent to S at the beginning of a simulation. INIT_OUTFLOW in
eq 45 is equivalent to O in the second part of eq 39 at the beginning of a simulation:
SBS_STORt1 = SBS_STORt 0 + dt(INFLOW_II∆t - OUTFLOW_II∆t )
(40)
INFLOW = I
(41)
I = 0.2778 DA P FATR PCT_2
where
(42)
OUTFLOW_II = GD_SBS_STOR / KSSa
(43)
INIT_SBS_STOR = INIT_OUTFLOW KSSa
(44)
INIT_OUTFLOW = QSS DA PCT_2 FATR
(45)
TECHNICAL DESCRIPTION OF SRFRNF
Overland runoff routing is calculated within the sector called "SRFRNF." Overland runoff rout-
ing is accomplished by summing the surface runoff generated from each of the runoff generation
sectors (GROFF1, GROFF2, GROFF3, GROFF4, and GROFF5) and delaying the flow of the runoff
sum to simulate the average time required for all runoff to leave the watershed. The runoff delay is
accomplished by routing the runoff sum through a linear reservoir and then a lag and route structure
(Veissman et al. 1977). The name, brief description, initial condition, and units of each variable
featured in this section are listed in Table 14.
The values for KL, KOa, and TLO were derived from p. 5-11 of the GAWSER training manual.
KL is equivalent to the sum of TMC plus 1/2 (TOC) from page 5-11. KOa is identical to KO in the
manual. TLO equivalent to TLO in the manual. The units for RSUM are m3 h/s because it is calculat-
ed on an hourly basis and is incremented by SRF_RUNOFF whose units are in m3/s. The rest of the
values are equal to zero because they calculate the amount of runoff that is not initially generated in
this example (Schroeter 1989).
Figure 21 is the structural diagram which contains the equations that perform runoff routing. The
linear reservoir includes INFLOW_5, LIN_RES_STOR, OUTFLOW_5, and KL. The input to the
linear reservoir structure, INFLOW_5, contains the sum of SURF1w, SURF2w, SURF3w, SURF4w,
and SURF5w. The lag and route structure includes INFLOW_2, LG_RT_STOR, OUTFLOW_2,
KOa, OUTFL_2_LAG, and TLO. The input to the lag and route structure, INFLOW_2, contains the
value of OUTFLOW_5, output from the linear reservoir structure. The final output from the lag and
route structure, OUTFL_2_LAG, is converted from mm/h to m3/h within SRF_RUNOFF. RSUM
calculates the total surface runoff from the watershed.
Equations 4648 are the linear reservoir routing equations in Object-GAWSER that route runoff
and are derived from eq 38 and 39:
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