Recession Constant Example

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