Modified Rational Formula

The modified rational formula used to estimate peak flow rate is obtained by substituting equations 2:1.3.15, 2:1.3.16, and 2:1.3.17 into equation 2:1.3.1

$q_{peak}=\frac{\alpha_{tc}*Q_{surf}*Area}{3.6*t_{conc}}$ 2:1.3.20

where $q_{peak}$ is the peak runoff rate ($m^3 s^{-1}$), $\alpha_{tc}$ is the fraction of daily rainfall that occurs during the time of concentration, $Q_{surf}$ is the surface runoff (mm H$_2$O), $Area$ is the subbasin area (km$^2$), $t_{conc}$ is the time of concentration for the subbasin (hr) and 3.6 is a unit conversion factor.

Table 2:1-5: SWAT+ input variables that pertain to peak rate calculations.

Variable Name	Definition	Input File
SUB_KM	Area of the subbasin (km$^2$)	.sub
HRU_FR	Fraction of subbasin area contained in HRU	.hru
SLSUBBSN	$L_{slp}$: Average slope length (m)	.hru
HRU_SLP	$slp$: Average slope steepness (m/m)	.hru
OV_N	$n$: Manning’s “n” value for overland flow	.hru
CH_L(1)	$L$: Longest tributary channel length in subbasin (km)	.sub
CH_S(1)	$slp_{ch}$: Average slope of tributary channels (m/m)	.sub
CH_N(1)	$n$: Manning’s “n” value for tributary channels	.sub