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 (m3/s) 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-to), lnQ(t)). This is accomplished below.

 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-to), lnQ(t)), t > 13 h, the recession constant is obtained as k = 0.249.