# 2:1.3.4 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.

| Definition                                               | Source Name | Input Name | Input File |
| -------------------------------------------------------- | ----------- | ---------- | ---------- |
| Area of the subbasin (km$$^2$$)                          | SUB\_KM     |            | .sub       |
| Fraction of subbasin area contained in HRU               | HRU\_FR     |            | .hru       |
| $$L\_{slp}$$: Average slope length (m)                   | SLSUBBSN    |            | .hru       |
| $$slp$$: Average slope steepness (m/m)                   | HRU\_SLP    |            | .hru       |
| $$n$$: Manning’s “n” value for overland flow             | OV\_N       |            | .hru       |
| $$L$$: Longest tributary channel length in subbasin (km) | CH\_L(1)    |            | .sub       |
| $$slp\_{ch}$$: Average slope of tributary channels (m/m) | CH\_S(1)    |            | .sub       |
| $$n$$: Manning’s “n” value for tributary channels        | CH\_N(1)    |            | .sub       |