## How to Calculate Annual Runoff?

**Mathematical Problem:**

For a catchment in M.P., India, the mean monthly rainfall and temperatures are given. Calculate the annual runoff by Khosla’s formula.

Month | Jan | Feb | Mar | Apr | May | June | July | Aug | Sep | Oct | Nov | Dec |

Temp (°C) | 12 | 16 | 21 | 27 | 31 | 34 | 31 | 29 | 28 | 29 | 19 | 14 |

Rainfall | 4 | 4 | 2 | 0 | 2 | 12 | 32 | 29 | 16 | 2 | 1 | 2 |

**Solution:**

In Khosla’s formula,

R_{m} = P_{m} – L_{m}

Where,

- R
_{m}= Monthly runoff - P
_{m}= Monthly rainfall in cm - L
_{m}= (0.48 × T) Or P_{m}whichever is less. - T = Monthly temperature in degrees.

**1. For January month**

L_{m} = (0.48 × 12) = 5.76

So, 5.76 is greater than the corresponding P_{m} = 4.

So, the value of L_{m} will be taken as 4.

Now,

R_{m} = (P_{m} – L_{m}) = (4 – 4) = 0

2. For July month

L_{m} = (0.48 × 31) = 14.88

So, 14.88 is less than the corresponding value of P_{m} = 32

So, we will take the value of L_{m} = 14.9

Now,

R_{m} = (P_{m} – L_{m}) = (32 – 14.88) = 17.1

I think you can able to solve the rest of the months by using the above method.

Month | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |

Rainfall (P_{m}) | 4 | 4 | 2 | 0 | 2 | 12 | 32 | 29 | 16 | 2 | 1 | 2 |

Temp (°C) | 12 | 16 | 21 | 27 | 31 | 34 | 31 | 29 | 28 | 29 | 19 | 14 |

L_{m} | 4 | 4 | 2 | 0 | 2 | 12 | 14.9 | 13.9 | 13.4 | 2 | 1 | 2 |

R_{m} | 0 | 0 | 0 | 0 | 0 | 0 | 17.1 | 15.1 | 2.6 | 0 | 0 | 0 |

So, the total annual runoff = ( 17.1 + 15.1 + 2.6) = 34.8 in cm.

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