1. Estimating Groundwater Availability at the Catchment
Scale Using Streamflow Recession and Instream
Flow Requirements of Rivers in South Africa
Girma Y. Ebrahim
Karen G. Villholth
IUGG 26th conference,
Prague, Jun 22- July 2,
2015

2. Introduction
• Groundwater (GW) is a critical source of water for
domestic consumption, agriculture, and industrial
development in South Africa
• Besides that, GW is of vital importance for securing
functioning and biodiversity of ecosystems
• As demand for water continues to increase there is
potential for conflict between human and ecosystem
needs
• Traditionally, GW allocation has ignored the
requirements of GW-dependent ecosystems and
made no provision for a water regime that might
sustain them

3. Introduction…
• In the National Water Act of South Africa of 1998,
the GW components of the Reserve are:
– that part required to satisfy basic human needs
(the GW component of the BHN Reserve), and
– that portion required to protect the aquatic
ecosystems (the GW component of the
environmental Reserve) (Xu et al., 2003)
• Further allocation of GW to beneficial uses can only
be granted once GW has been set aside for the
Reserve

4. Objectives
• The overall aim of this study is to develop and test an
integrated method for assessing allocable GW (for
all uses) from stream flow recession and instream
flow requirements
• Apply the method to selected quaternary catchments
in South Africa

5. Assumptions
• Baseflow = groundwater contribution to the river
• Groundwater contribution to environmental
requirements = Maintenance low flow requirements
(MLIFR)
• Shallow aquifer acts as a linear reservoir
• Allocatable groundwater = annual baseflow - MLIFR

6. Steps in Method
1. Select streamflow gauging stations and study sites
2. Determine drainage time scale K from recession flow
3. Determine the river baseflows through a baseflow
separation method
4. Determine MLIFR using the desktop reserve model (DRM)
5. Determine the surplus baseflow (annual baselflow - MLIFR)
6. Convert the surplus baseflow to equivalent GW storage
thickness, using the drainage time scale K (S=KQ)
7. Determine the upper limit of groundwater abstraction as the
GW storage thickness equalled or exceeded 75% of the
years from the storage thickness duration curve

7. Selection of study sites
• Quaternary catchments were selected using the following
criteria
 Long-term (>30 years) daily stream flow data
 Long-term baseflow index (BFI) should be higher than
0.25 (based on map in Hughes et al. (2007)). BFI is a
proportion of baseflow to total streamflow
 Catchments should be relatively pristine
 Missing data should be less than 10%
• These criteria were quite strict (identifying only 1.7% of
the stations in the database)
• The selected catchments varied in size from 23 to 697 km2,
and annual rainfall from 526 to 1058 mm.

8. Selected quaternary catchments

9. Geological conditions of the selected sites
Percentage area of the quaternary catchment covered by certain lithology
Zone-3Zone-2Zone-1

10. Estimating drainage time scale from
recession flow analysis
• Recession analysis is a well-known tool in hydrological
analysis
• The Boussinesq equation describing flow in unconfined
aquifers based on the hydraulic approach is shown in
Brutsaert and Nieber (1977) to be expressed in general
as a power law function:
•
𝑑𝑄
𝑑𝑡
= −𝑎𝑄 𝑏 (1)
• During low flow, b=1 and the flow recession is
approximated as an exponential decay function (linear
reservoir) (Brutsaert and Lopez, 1998)
• S= KQ (2)
Adopted from Rupp and
Selker (2005)

11. Estimating drainage time scale from
recession flow analysis
• From Eq. 1 and assuming a linear reservoir
approximation:
log(−
𝑑𝑄
𝑑𝑡
) = log 𝑎 + log(Q ) (3)
• When daily values of -dQ/dt and Q are plotted on
log-log graph, the cluster of the points is ‘enveloped’
by a lower line of slope equal to 1
• The envelope line represents the lowest recession
rate (-dQ/dt) for a given Q, which is considered the
baseflow condition

12. Extracted recession points from streamflow
and lower envelope line
Extracted recession flow data
points and the total streamflow
Lower envelope line
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13. Baseflow separation
• The recursive digital filter by Nathan and McMahon
(1990)
 𝑞𝑡 = 𝛽𝑞𝑡−1 +
1+𝛽
2
∗ (𝑄𝑡 − 𝑄𝑡−1) (4)
 Where qt is the filtered surface runoff at time step
t, Qt is the original streamflow at time t, and β is
the filter parameter
• Baseflow bt is calculated as:
 𝑏𝑡 = 𝑄𝑡 − 𝑞𝑡 (5)

14. Baseflow separation and baseflow index
• The value of β ranges
from 0.90 to 0.95, while a
β value of 0.925 is
recommended as optimal
• For rivers in South Africa,
Smakhtin and Watkins
(1997) recommended
0.995 as being suitable
for daily baseflow
separation
• We used β = 0.995
6/25/2015 14

15. Estimating environmental flow requirements
using the Desktop Reserve Model (DRM)
• DRM uses two Index of flow variability
• CVB=CV/BFI
• DRM computes maintenance low instream flow
requirements (MLIFR) as a percentage MAR using
the following relation (Hughes and Hannart, 2003)
• 𝑀𝐿𝐼𝐹𝑅 = 𝐿𝑃4 +
𝐿𝑃1 𝑥 𝐿𝑃2
(𝐶𝑉𝐵 𝐿𝑃3) 1−𝐿𝑃1 (6)
 Where LP1, LP2, LP3 and LP4 are parameters
which need to be determined for a particular level
of ecological category [A-D]

16. Present ecological conditions of rivers
Quaternary
catchment ID
River gauge
ID
Present
Ecological
state
Quaternary
catchment ID
River gauge
ID
Present
Ecological state
B81D B8H010 C K80C K8H001 C
A42D A4H008 B K80C K8H002 C
B73A B7H004 C K70B K7H001 B
B42F B4H005 C K60A K6H001 B
B11K B1H004 C K50A K5H002 B
C81F C8H005 C K40B K4H001 B
V60A V6H004 A K40C K4H002 B
U20D U2H006 B K30D K3H005 B
U20B U2H007 C K30A K3H003 C
U20A U2H013 B K20A K2H002 C
U70A U7H007 C
Zone-1 Zone-2 Zone-3

17. Analysis and Results
Drainage time scale (K) and BFI
Drainage time scale (K) BFI
K ranges from 28 to 168 days
BFI ranges from 0.14 to 0.54
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18. Analysis and Results
Correlation of K with catchment attributes
Area
(km2)
River
length
(m)
Drainage
density
(km-1)
Slope
(%)
Mean
elevation BFI
Water
level
(amsl)
K
days
Area (km2) 1.00
River length
(m) 0.91 1.00
Drainage
density (km-1) 0.19 0.57 1.00
Slope (%) -0.20 -0.06 0.20 1.00
Mean
elevation 0.69 0.63 0.16 -0.34 1.00
BFI 0.17 0.08 -0.08 -0.75 0.51 1.00
Water level
(amsl) 0.50 0.43 0.11 -0.49 0.89 0.75 1.00
K (days) 0.06 -0.11 -0.31 -0.80 0.47 0.92 0.69 1.00

19. Analysis and Results
MLIFR and MAR
MLIFR ranges from 6-26% of MAR

20. Analysis and Results
Upper limit of groundwater allocation
Annual groundwater storage
thickness
Duration curves for groundwater
storage thickness
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Variability b/n years is assumed to be manageable
through buffering capacity of GW

21. Analysis and Results
Groundwater storage thickness

22. Conclusions
• The methodology is based on simple assumptions and
concepts, implying uncertainties. However, it is useful for
first estimates in GW data-scarce regions
• The method accounts for inter-annual variability of
stream flow
• In 17 out of 21 catchments assessed, opportunities exist
to further utilise GW
• The method needs to be tested against current GW
assessment and allocation tools and supplemented by
GW monitoring data - for method refinement and for
compliance and future impact assessment

23. References
1. Brutsaert, W., and Lopez, J. P., 1998, Basin-scale geohydrologic drought flow features of
riparian aquifers in the southern Great Plains: Water Resources Research, v. 34, no. 2, p.
233-240.
2. Brutsaert, W., and Nieber, J. L., 1977, Regionalized drought flow hydrographs from a
mature glaciated plateau: Water Resources Research, v. 13, no. 3, p. 637-643.
3. Hughes, D. A., and Hannart, P., 2003, A desktop model used to provide an initial estimate
of the ecological instream flow requirements of rivers in South Africa: Journal of
Hydrology, v. 270, no. 3, p. 167-181.
4. Hughes, D. A., Parsons, R., and Conrad, J. E., 2007, Quantification of the groundwater
contribution to baseflow, Water Research Commission.
5. Nathan, R. J., and McMahon, T. A., 1990, Evaluation of automated techniques for base
flow and recession analyses: Water Resources Research, v. 26, no. 7, p. 1465-1473.
6. Rupp, D. E., and Selker, J. S., 2005, Drainage of a horizontal Boussinesq aquifer with a
power law hydraulic conductivity profile: Water resources research, v. 41, no. 11.
7. Smakhtin, V. U., and Watkins, D. A., 1997, Low-flow estimation in South Africa. Water
Research Commission Report N 494/1/97, Vol 1; Vol 2: Appendices.
8. Xu, Y., Colvin, C., van Tonder, G., Hughes, S., Le Maitre, D., Zhang, J., Mafanya, T., and
Braune, E., 2003, Towards the resource directed measures: groundwater component
(Version 1.1): WRC Report.

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