**CE322 Basic Hydrology**

Jorge A. Ramirez

**Recession Constants - Example**

Obtain the groundwater recession constant using the following data. The table below presents the recession limb of a total streamflow hydrograph.

Time (h) |
Streamflow Hydrograph (m |

10 |
2000 |

11 |
993 |

12 |
493 |

13 |
245 |

14 |
191 |

15 |
149 |

16 |
116 |

17 |
90 |

18 |
70 |

19 |
55 |

20 |
43 |

Assuming that the basin responds as a linear reservoir, the recession limb of the hydrograph is described by the following:

where *k* is the recession constant of the system. Observe that this equation is linear in the semi-log
domain:

Therefore, the recession constant *k* can be estimated as the negative of the slope of a least-squares
fit to the pairs (*(t-t _{o})*,

Time (h) |
Streamflow Hydrograph (m3/s) |
ln(Q(t)) |

10 |
2000 |
7.600902 |

11 |
993 |
6.900731 |

12 |
493 |
6.200509 |

13 |
245 |
5.501258 |

14 |
191 |
5.252273 |

15 |
149 |
5.003946 |

16 |
116 |
4.75359 |

17 |
90 |
4.49981 |

18 |
70 |
4.248495 |

19 |
55 |
4.007333 |

20 |
43 |
3.7612 |

Because there exist several distinct storages in a basin, the recession limb of hydrographs includes contributions
from all of those storages. Thus, the procedure outlined above can be used sequentially to obtain the corresponding
recession constants for each one of the storages (*e.g.*, groundwater storage, subsurface storage). The existence
of the different storages is easily observable in the semi-log domain as shown in the graph below.

In the graph below, observe that the slowest portion of the recession starts at time *t* = 13 h. Thus,
we can use the streamflow data for *t* > 13 h to estimate the groundwater recession constant. Using least
squares on *((t-t _{o}), lnQ(t)), t* > 13 h, the recession constant is obtained as