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.