# 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       |


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://swatplus.gitbook.io/io-docs/~/changes/GiVD5ID0WVyRIAumaMy2/surface-runoff/modified-rational-formula.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.