Trends in Rainfall and Runoff in the Blue Nile Basin: 1964-2003
Zelalem K. Tesemma1, Yasir A. Mohamed2, 3, Tammo S. Steenhuis 1,4
1
Integrated Watershed Management and Hydrology Master’s Program, Cornell University, Bahir Dar,
Ethiopia.
2
International Water Management Institute, IWMI-NBEA, PO Box 5689, Addis Ababa, Ethiopia.
3
UNESCO-IHE Institute for Water Education, P.O. Box 3015, 2601DA Delft, Netherlands.
4
Biological and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA.
Abstract
Most Nile water originates in Ethiopia but there is no agreement on how land degradation or climate
change affects the future flow in downstream countries. The objective of this paper is to improve
understanding of future conditions by analyzing historical trends. During the period 1963 to 2003, average
monthly basin wide precipitation and monthly discharge data were collected and analyzed statistically for
two stations in the upper 30% of Blue Nile Basin and one station at the Sudan-Ethiopia border. A rainfall
runoff model examined the causes for observed trends. The results show that while there was no significant
trend in the seasonal and annual basin-wide average rainfall, significant increases in discharge during the
long rainy season (June to September) at all three stations were observed. In the upper Blue Nile the short
rainy season flow (March to May), increased while the dry season flow (October to February) stayed the
same. At the Sudan border the dry season flow decreased significantly with no change in the short rainy
season flow. The difference in response was likely due to weir construction in the nineties at the Lake
Tana outlet that affected significantly the upper Blue Nile discharge but only affected less than 10% of the
discharge at the Sudan border. The rainfall runoff model reproduced the observed trends, assuming that an
additional ten percent of the hillsides were eroded in the 40 year time span and generated overland flow
instead of interflow and base flow. Models concerning future trends in the Nile cannot assume that the
landscape runoff processes will remain static.
Key words: Climate change, Watershed hydrology, Model, Rainfall-Runoff models, Blue Nile.
1
be an effective method. (Yilma and Demarce,
Introduction
1995;; Kim, 2008; Conway, 2000) especially if
The Nile basin is one of the most water-limited
these trends can be related to changes in land use
basins in the world. Without the Nile major
and rainfall.
portions of Sudan and Egypt would run out of
water. There is a growing anxiety about climate-
Previous
induced changes of the river’s discharge,
regressions over time to detect trends in annual
especially because Ethiopia, which generates
runoff and rainfall series without removing the
85% of the annual Main Nile flow (Sutcliffe and
seasonal effects or trying to predict seasonal
Parks,
differences
1999),
is
actively
planning
major
studies
in
employed
discharge
simple
(Conway,
linear
2000;
hydropower and irrigation development. To
Sutcliffe and Parks, 1999). The objective of this
develop appropriate adaptation strategies to relay
research is therefore to improve on these
these concerns, long-term trends in stream flow
predictions by using both the Mann-Kendall and
should be investigated (Conway, 2000; Conway
Sen’s T test to detect trends in both seasonal and
and Hulme, 1993 1996; Yilma and Demarce,
annual runoff and rainfall and then using a semi-
1995; Kim et al., 2008), which requires a better
distributed rainfall runoff model to both confirm
understanding of the basin’s hydrology and
that the rainfall runoff relationship is changing
embedded long-term variability
over to forty year period and to find the
underlying physical conditions that explains the
The literature shows an increasing number of
observed runoff trends.
climate change studies in the Nile basin (e.g.,
Conway and Hulme 1993, 1993; Conway, 2000;
The Blue Nile Basin
Elshamy et al., 2009; Strzepek et al., 1996; Kim
et al., 2008). Impact of climate change on Blue
The Upper Blue Nile River (named Abbay in
Nile discharge was highly variable in these
Ethiopia) starts at Lake Tana and ends at the
studies. One of the reasons is that the Global
Ethiopia-Sudan border. The topography of the
Circulation Models cannot even agree on the
Blue Nile is composed of highlands, hills,
sign(s) of change (Elshamy et al., 2009).
valleys and occasional rock peaks. Most of the
Therefore,
by
streams feeding the Blue Nile are perennial. The
studying past trends of rainfall and discharge can
average annual rainfall varies between 1200 and
predicting
future
scenarios
2
1800 mm/yr (Figure 1 a), ranging from an
May; and long rainy period (Kiremt) from June
average of about 1000 mm/year near the
to September, with the greatest rainfall occurring
Ethiopia/Sudan border,to1400 mm/yr in the
in July and August. The year to year variation in
upper part of the basin, and in excess of 1800
monthly rainfall is most pronounced in the dry
mm/yr in the south within Dedessa subbasin
season,
(Conway 2000; Sutcliffe and Parks, 1999).
occurring in the rainy season. Interannual
Locally the climatic seasons are defined as: dry
variability of rainfall in the basin is 10% (Table
season (Bega) from October to the end of
1).
with
the
lowest
annual
variation
February; short rain period (Belg) from March to
Table 1: The seasonal Mann-Kendall and Sen’s T tests statistics for Upper Blue Nile basin
hydroclimatology record from1963 to 2003.
UB Station
Rainfall
( mm)
Areal rainfall
Runoff
( ( Billion m3)
Bahir Dar
Kessie
El Diem
Seasons
Mean1
CV2
(%)
z Test3
T test4
Annual
Dry
Short rainy
Long rainy
1286
151
218
916
10
36
26
10
-0.5
-0.6
0.6
-0.2
-0.5
-1.1
0.5
-0.7
Annual
Dry
Short rainy
Long rainy
3.8
2.0
0.3
1.5
36
33
100
45
2.0
0.6
3.2
2.7
3.3
0.9
2.4
2.6
Annual
Dry
Short rainy
Long rainy
16.0
3.2
0.6
12.2
31
30
60
35
2.2
0.8
3.2
3.6
3.8
1.0
3.2
2.7
Annual
Dry
Short rainy
Long rainy
46.9
11.0
1.3
34.6
Slope5
(106 m3 / yr)
Change6
(Billion m3)
Change7
(%)
2.1
9.8
0.08
0.39
33
26
109.0
4.36
27
7.2
83.7
0.288
3.35
51
27
20
0.5
0.3
32
-28.3
-1.13
-2.5
-2.4
34
0.8
0.7
19
87.7
3.52
3.0
2.0
Note: Bold figures are significant at 5% significance level.
Short rainy season (March-May); Long rainy season (June –
Dry season (Oct-Feb);
September)
1= Mean of the seasonal total runoff/rainfall (1964-2003).
2= coefficient of variation (1964-2003).
3=the Mann-Kendall test statistics.
4=Sen’s T test statistics.
5=Sen’s slope estimator.
6=calculated as slope times years of record (40 years).
7=calculated as change over the respective mean seasonal runoff
3
-10
10
The
long-term
annual
1997). There is uncertainty about how forest
discharge of Blue Nile entering Sudan and
cover has changed over the last 50 years. Some
measured at Roseires/El Diem is 48.9 *109 m3/yr
report a decrease (USBR, 1964; Mohammed,
which is about 60% of the flow of Main Nile
2007) while Bewket (2002) showed that green
(Sutcliffe and Parks, 1999), with flows of
cover has increased since 1950 over the 364 km2
3.9*109 m3/yr at Bahir Dar (1959-2003) and 16.3
Chemoga watershed in the upper Blue Nile
*109 m3/yr at Kessie (1953-2003) respectively
basin.
(Figure 1b).
(1912-2003)
The
distribution
mean
of seasonal
Input for statistical analysis and rainfall
discharge varies considerably (Figure 1c). The
runoff modeling
average discharge at El Diem is smallest in April
and greatest in August, about 35 times the April
flow. The annual variability of stream flow
varies
Input Data
Monthly data were collected for statistical
analysis, and modeling required 10-day data.
Monthly rainfall data for statistical analysis were
downloaded from Global Historical Climatology
Network (NOAA, 2009) and the 10-day rainfall
data for the selected stations (shown in Figure 2)
were obtained from the National Meteorological
by less than 20% (Conway and Hulme, 1993;
Conway, 2000; Yilma and Demarce, 1995).
Most of the soil types covering the Blue Nile
basin are volcanic vertisols or latosols (Conway,
Services Agency of Ethiopia. Monthly stream
4
flow data were obtained from the Hydrology
UNESCO/IHP
Department of the Ministry of Water Resources
http://dss.ucar.edu/datasets/ds553.2/data/.
of Ethiopia, and Ministry of Irrigation and Water
the data available, three stream flow gages
Resources of Sudan and the Global Hydro
(Figure 2) were selected that had more than 25
Climate
years data, which is sufficiently long to yield
Data
Network
operated
by
available
at
From
statistically valid trends (Burn and Elnur, 2002).
decimal
Of these, the gaging station at El Deim at the
identified by comparison with upper and a lower
Sudanese Ethiopian border had the longest and
boundary limits. Values outside the limits were
most reliable record, extending from 1912 to
further validated by comparing the data plots of
present (Conway, 2000; Sutcliffe and Parks,
neighboring stations. The confirmed suspect
1999). The Kessie hydrometric station is located
values were removed and replaced by values
near the bridge where the main road to Addis
derived by a relation curve with neighboring
Ababa from Bahir Dar crosses the Abbay (Blue
station(s). Missing data of the rainfall were fitted
Nile) river, with discharge data recorded since
using best fit regression with neighboring
1953. Except for the last few years during the
stations.
digits
were
fixed.
Outliers
were
bridge construction, the data is fair to good
(Conway, 2000). The third station is downstream
Methodology
of the outlet of Lake Tana in Bahir Dar. The
construction in 1996 of the Chara-Chara weir for
Both statistical analysis and a semi-distributed
generating
the
rainfall runoff model were used to assess trends
discharge by storing water in Lake Tana during
in the discharge in the Blue Nile basin. The
the wet season and releasing it during dry season.
statistical analysis of trends in climate and
hydropower
has
affected
hydrologic variables uses the Mann-Kendall test
Data validation and completion
(Zhang et al, 2001; Huth and Pokorna, 2004;
After the raw rainfall and discharge data were
Harry et al, 1999). To gain more confidence in
collected, a thorough checking and validation
our results, a categorically different and less
was performed. First the data were visually
common technique, Sen’s T test, was employed
screened, and mistyped numbers and misplaced
as well (KarabÖrk, 2007). Both tests are non-
assumptions about the distribution of the
parametric approaches and do not require any
variables.
5
widely to identify trends in hydroclimatic
Mann-Kendall test
variables (see e.g., Kahya and Kalayci, 2004; Xu
The Mann-Kendall (Mann, 1945; Kendall, 1975)
et al., 2003; Partal and Kalya, 2006; Yue and
test is a rank-based method that has been applied
Hashimoto, 2003). Following Burn et al. (2004),
we
have
corrected
the
data
for
serial correlation through a modified version of
percent chance for error exists in concluding that
the Trend Free Pre-Whitening (TFPW) approach
a trend is statistically significant when in fact no
developed by Zhang et al. (2001) and Yue et al.
trend exists.
(2002). The TFPW approach attempts to separate
the serial correlation that arises from a linear
trend from the original time series. This involves
Rainfall-Runoff modeling
estimating a monotonic trend for the series,
Statistical tests examine rainfall and discharge
removing this trend prior to Pre-Whitening the
separately. Rainfall runoff models can establish,
series and finally adding the monotonic trend
if the relationship between rainfall and discharge
back to the Pre-Whitened data series to remove
has changed over time and may indicate the
the serial correlation.
underlying physical mechanisms if a change has
occurred.
Sen’s T test
The test statistic “T” is computed under the null
The runoff model used here is a semi distributed
hypothesis of no trend, the distribution of T tends
rainfall-runoff model (validated by Steenhuis et
toward normality with mean Zero and unit
al., 2009 for the Blue Nile Basin) in which
variance
detailed
various portions of the watershed become
computational procedure of the test statistic is
hydrologically active after the dry season when a
given in Van Belle and Hughes, (1984).
threshold moisture content is exceeded. In the
(Sen,
1968a,
b).
The
model, the permeable hillslope contribute rapid
All the trend results in this paper have been
subsurface flow (called interflow) and base
evaluated at the 5% level of significance to
flow.. For each of the three regions, a
ensure an effective exploration of the trend
Thornthwaite Mather-type water balance is
characteristics within the study area. The 5-
calculated. Surface runoff is generated when the
percent level of significance indicates that a 5-
soil is saturated and assumed to be at outlet
6
within the time step. The percolation is
Calibration
calculated as any rainfall when the hillside soil is
changing the parameter values in small steps
at field capacity. Zero and first order reservoirs
around the values found earlier by Steenhuis et al
determine the amount of water reaching the
(2009) for the Blue Nile basin. The model was
outlet. Equations are given in Steenhuis et al.
calibrated for two three-year periods 34 years
(2009) and reproduced in the auxiliary material
apart: 1964-1966 and 1998- 2000. Validation
in Appendix A.
was done in the subsequent three years for each
was
performed
by
manually
period: 1967-1969 and 2001-2003. To test if the
Two types of input data are needed: climate and
parameter values had changed over the 34 year
landscape. Climate input data consisted of 10-
period, the calibrated parameters set for the early
day rainfall amounts that were obtained by
period was compared with the observed flow for
averaging the 10-daily rainfall of the selected 10
the later period. Similarly the calibrated data for
rainfall gauging stations using the Thiessien
the latter period was run for the early period.
polygon method (Kim et al., 2008). The potential
evaporation was set according to Steenhuis et al
Results and Discussion
(2009) at values of 3.5 mm/day for the long rainy
season (June to September) and 5 mm/day for
Trend analysis results
the dry season (October to May). These values
The annual areal rainfall over the basin (CV =
were selected based on the long-term average of
10%) is less variable (column 4 in Table 1) than
available potential evaporation data over the
the stream flow at all the stations. The opposite
basin. As landscape input parameters for the
is true for the dry (October to February) and
model, the relative areas of the three regions are
short rainy season (March to May) while the
needed as well as the amount of water (available
long
for evaporation) between wilting point and the
precipitation is less variable than the rainfall
rainy
season(June
to
September)
threshold moisture content. In addition, the
interflow and baseflow rate constants were part
Precipitation: Both the Mann-Kendall and Sen’s
of the input data set. The landscape parameter
T indicate that there was no significant trend
values cannot be determined a priori and need to
level in the basin wide annual, dry season, short
be obtained by calibration.
and long rainy season rainfall at 5% significant
level for the Blue Nile basin for the period from
7
1963-2004 (column 5 & 6 of Table 1) Our results
Kessie and 10% at El Diem. Discharge during
are in agreement with Conway (2000) who did
the
not find either a tendency towards wet or dry
significantly at 33% at Bahir Dar and 51% at
condition.
Kessie, while the trend was not significant at El
short
rainy
season
stream
increased
Diem in the period from 1963 to 2003 (Table 1).
Discharge: The trends in stream flow computed
The possible reason for this phenomena could be
by the Mann-Kendall test and Sen’s T test are
analysis of low values may retrieve drastic
similar (Table 1). The agreement of the two
results and effect of the Chara-Chara weir after
different tests shows that the results are robust
1996.
and both indicate that there was no significant
showed no significant trends at Bahir Dar and
trend in the observed annual runoff at El Diem at
Kessie but a significant decreasing trend at El
the Sudan border. This is consistent with the
Diem by 10% (Table 1). Despite differences in
observation at that point that the basin-wide
rainfall pattern, the analysis clearly shows
annual rainfall remained the same and potential
differences in runoff pattern over the 40 year
evaporation from year to year usually does not
period. For the two upper Nile stations, Kessie
vary. The annual discharge, therefore, which is
and Bahir Dar the increased annual discharge is a
the difference between rainfall and evaporation -
consequence of the increased discharge during
a unique function of rainfall and potential
the two rainy periods while the dry season flow
evaporation- should stay the same for a given
is not affected. For El Deim, where the annual
annual rainfall amount. Somewhat surprising is
flow remained constant over the 40 years, the
the fact that the annual discharge at Kessie (with
increase in discharge during the wet season is
1/3 the discharge at El Diem) and Bahir Dar
canceled by a decrease of flow during the dry
increased significantly by about 25 percent over
period. The results at Kessie and Bahir Dar
the 40 year period.
(especially during low flow conditions) are
Finally, the dry season stream flow
affected by installation of the Chara Chara weir
Despite the difference in annual trends, all three
at the outlet of Lake Tana during the last 7 years
stations show significant increasing discharges
of the record analyzed, which increased flow
over time during the long wet season. As a
during the dry season to provide water for the
percentage of the 40-year seasonal mean, these
hydropower plant at the Nile Falls. It also
increments were 26% at Bahir Dar, 27% at
decreased the flow during the rainy season but,
8
despite that, the discharge during the rainy
correspond most closely when the hillside
period still increased according to our analysis.
(recharging the interflow and groundwater) made
Our results for the Upper Blue Nile agree in part
up 70% of the landscape and with a soil water
with those of Bewket and Sterk (2005) in the
storage of 250 mm (between wilting point and
Chemoga watershed, which is not affected by
field capacity). Surface runoff was produced
Chara-Chara weir where during the wet season
from the exposed surface or bedrock making up
the discharge increased with time but decreased
10% of the landscape and saturated areas
during the dry season, giving creditability to the
comprising 20% of the area (Table 2, Figure 3).
assumed effect of the Chara Chara weir on
After the dry season, the exposed bedrock
increasing the low flows.
needed to fill up a storage of 25 mm before it
became hydrologically active, whereas the
Rainfall Runoff simulation
saturated areas required 200 mm. Parameter
Rainfall-Runoff modeling can establish if the
calibration for the period from 1998 to 2000
relationship between rainfall and runoff are exist.
showed
In addition, underlying hydrological mechanisms
coverage to 20% and decreasing the hillslopes by
for altered discharge can be identified (Mishra et
10% to 60% gave the best fit while all other
al., 2004). Since the flow at Bahir Dar and
parameters could be kept the same (Table 2,
Kessie is most affected by the Chara-Chara weir,
Figure 3). The Nash-Sutcliffe model efficiencies
we used the gauge at El Diem to establish the
were remarkably high for such a simple model:
relationship. Calibration of the parameters was
0.92 and 0.91 for the calibration periods and 0.87
based on the assumption the subsurface flow
and 0.86 for the validation periods, respectively
parameters (interflow and baseflow) remain the
for the first and second time periods, (Table 3,
same over time, as does the storage of the
a). Similarly, good correlation coefficient r2, and
landscape components. Thus the only calibration
small Root Mean Square Errors were obtained
parameter to characterize the flow in the 1960’s
for selected set of calibration an validation
and at the end of the 1990’s is the amount of
parameters (Table 3, a). The high runoff Nash-
degraded soils that produce surface runoff in the
Sutcliffe efficiencies are an indication that
1990’s
calibrated
although simple, the model effectively captured
parameter values are shown in Table 2. For the
the hydrological processes in which various
1964-1969 the observed and predicted values
portions of the watershed become hydrologically
and
around
2000.
The
that
increasing
exposed
bedrock
9
active after the dry season, as proposed by
1990’s, the model was run by interchanging the
Collick et al (2009)
calibrated model parameters between the two
periods. The results showed that the accuracy of
To further confirm whether model parameters
simulation decreased, i.e. results for all four
actually changed between mid 1960’s to late
simulation periods had Nash Sutcliffe values
below 0.86 (Table 3, b). Moreover, by
Table 2: Model input values for surface flow components, baseflow and interflow parameters.
Parameters
1964-1966
1967-1969
1998-2000
2001-2003
Calibration
Validation
Calibration
Validation
AR Exposed hard pan
0.1
0.1
0.2
0.2
AR Saturated bottom land
0.2
0.2
0.2
0.2
AR Hillslope zone
0.7
0.7
0.6
0.6
t* in (days)
200
200
200
200
t½ (half life) in (days)
30
30
30
30
Smax (Exposed hardpan)
25
25
25
25
Smax (Saturated bottom land)
200
200
200
200
Smax (Hillslope zone)
250
250
250
250
Note: AR = fraction area of the watershed
Smax = soil moisture storage (at field capacity or from dry to saturated) (mm).
t* = is the duration of the period after the rainstorm until the interflow ceases
t½ = the time it takes for half of the volume of the aquifer to flow out without the aquifer being
recharged.
Table 3: The model statistics computed for calibration and validation of discharge at El Diem.
a) three years calibration and three years validation for the first period 1964 to 1969 and the second period
1998 to 2003.
Parameters
Nash-Sutcliffe model eff. (e)
Correlation coefficient (r2)
RMSE mm/10 days
1964-1966
Calibration
0.92
0.92
2.70
1967-1969
Validation
0.87
0.88
3.36
1998-2000
Calibration
0.91
0.91
3.46
2001-2003
Validation
0.86
0.89
3.45
b) Parameters calibrated for the period 1964-1966 are used to predict the discharge for 1998-2003.
Similarly calibration parameters obtained for the period 1998-2000 are used to predict discharge for 19641969
Parameters
1998-2000
2001-2003
1964-1966
1967-1969
Validation
Validation
Validation
Validation
Nash-Sutcliffe model eff. (e)
0.85
Correlation coefficient (r2)
0.88
Root mean square error (RMSE)
3.63
Note: e=Nash-Sutcliffe efficiency coefficient.
r= coefficient of regression,
RMSE = Root mean square error
0.84
0.83
3.72
0.86
0.86
4.20
0.83
0.83
3.78
10
comparing observed versus predicted discharge
runoff and greater peaks than observed for the
in Figure 4 it becomes obvious that the calibrated
period of 1964-1969 (Figures 4a and 4b).
dataset of 1998-2000 period predicted earlier
Similarly, the calibrated data set for the 1960’s
11
predicted later runoff and lower peaks than
subsurface flow routines of the simple model are
observed around 2000 (Figures 4c and 4d). The
not
the observed differences in base flow during the
averaged
dry season. Despite that this model is based on a
watershed discharge. This relationship between
conceptual framework, it can be seen as
rainfall and watershed discharge clearly changes
arithmetical relationship that relate the spatially
over the 40 year period (Figures 3 and 4)
sufficiently
ten-day
sensitive
rainfall
to
to
predict
the
ten-day
12
indicating that the runoff mechanisms are
Trends of precipitation and discharge over a 40
shifting due to landscape characteristics since the
year period in Blue Nile basin have been
precipitation did not vary. However but cannot
investigated. The results show the precipitation
indicate what the reason is. The conceptual
did not change over the entire basin. Discharge
framework is needed to find the underlying cause
analysis for Bahir Dar and Kessie representing
for the observed shift in runoff pattern.
the upper part of Blue Nile and El Diem at the
border between Sudan and Ethiopia shows that
The conceptual framework leads to following
annual discharge increased for the upper Blue
explanation for the alteration in the runoff
Nile only. Discharge during the long rainy
pattern: Soil erosion during the period from the
season increased at all three stations. Discharge
early 1960’s to 2000, although occurring over
during the short rainy season increased due to the
the whole watershed, was more severe in certain
influence of the Chara-Chara weir at the outlet of
areas that caused the bedrock to be exposed. The
Lake Tana.
hillsides that were eroded in this period no
longer stored rainfall and released it later as
A simple rainfall runoff model calibrated for the
interflow as they had in the 1960’s but instead
beginning and end of the 40 year period showed
produced surface runoff in 2000. This in turn
that the peak in the runoff occurred earlier at the
caused a greater portion of the watershed to
end of this period than the beginning. This could
become hydrologically active at an earlier stage,
be explained by erosion of hillside lands that
releasing more of the rainfall sooner resulting in
stored some of the water before it became eroded
earlier flows and greater peak flow. These
and contributing areas of direct runoff. Further
simulation results are in line with the statistical
research is needed if other factors than the
result at the El Diem site which shows increasing
suggested changes could explain the statistical
trends of runoff during long or short rainy
and simulation results.
seasons but decreasing dry season runoff, while
annual flow has no significant change (see Table
Acknowledgements
1).
We extend sincere thanks to the Hydrology
Conclusions
Department of the Ministry of Water Resources
of Ethiopia and Sudan and the National
13
Meteorological Services Agency of Ethiopia for
materials and valuable comments. Financial
kindly providing us with the stream flow and
support was provided by IWMI project entitled:
rainfall data used for the study. We also would
‘Nile
Basin
Focal
Project
(NBFP).
like to thank Dr. Amy S. Collick for providing
References
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Auxiliary Material
APPENDIX A
Rainfall runoff model
two parts that either are degraded or have highly
permeable soils above a restricted layer at some
The landscape is divided into two parts, the well
depth. The degraded areas have the hardpan
drained hillslopes, and the relatively flatter areas
exposed at the soil surface. In these areas that
that become easily saturated during the rainfall
have restricted infiltration, a small amount of
season. The hillslopes are further divided into
water can be stored before saturation excess
15
surface runoff occurs. On the highly permeable
When precipitation, P, is less than potential
portion of the hillslopes most of the water is
evaporation Ep, water is withdrawn from the soil
transported
system
through
subsurface
as
rapid
by
soil
evaporation
and
plant
subsurface flow (e.g., interflow over a restrictive
transpiration. This result into the exponential soil
layer) or base flow (percolated from the soil
moisture depletion and is defined by the
profile to deeper soil and rock layers, McHugh,
following formula (Steenhuis et al., 2009):
2006).
surrounding hillslopes become runoff source
 ( P − E p )∆t 
S s (t ) = S s (t − ∆t ) exp 
,
 S max

areas when saturated (Fig. A1 shows a schematic
for P<Ep
The
flatter
areas
that
drain
the
(A2)
representation of a simplified hillslope). Three
separate water balances are calculated. The water
balance for the each of the three areas can be
written as
 S (t ) 
Ea = E p  s  ,
 S s max 
for P< Ep
(A3)
S s (t ) = S s (t − ∆t ) + [P − Ea − R − Perc ]∆t
On the hillslopes, areas with high infiltration
(A1)
capacity the excess water (Perc) becomes either
Where P is rainfall (LT-1), Ea the actual
interflow (Qif) or baseflow (Qbf) and is added to
evapotranspiration (LT-1), Ss(t) is storage water
their respective reservoirs, the interflow reservoir
in the soil profile at time t (L) above the
(Sif) and base flow reservoir (Sbf). Steenhuis et al
restrictive layer, Ss(t-∆t) is previous time step
(2009) assumed that first the base flow reservoir
water storage (L), R is saturation excess runoff
is filled, and when full (at a storage Sbfmax) the
(LT-1), Perc is percolation to the subsoil (LT-1)
interflow reservoir starts filling. The base flow
and ∆t is the time step (10 days in our case).
reservoir acts as a linear reservoir and its outflow
Percolation
(Qbf) when the storage is less than the maximum
occurs
on
the
non
degraded
hillslopes when the soil storage is more than
storage can be expressed as:
field capacity. Surface runoff on the saturated
bottom lands and degraded hill slopes occurs
Sbf (t ) = Sbf (t − ∆t ) + [ Perc − Qbf (t − ∆t )]∆t
when they are saturated is equal the amount
(A4)
rainfall minus the water that is needed to fill up
the soil to saturation.
16
Qbf (t ) =
S bf (t )[1 − exp[ −α∆t ]]
(A5)
∆t
Figure A1: Schematic for saturation excess overland flow, infiltration, interflow and baseflow for a
characteristic hill slopes in the Blue Nile Basin (after Steenhuis et al., 2009)
where α is the reservoir coefficient (L-1) and is
equal to 0.69/t½. When baseflow storage (Sbf) is
τ ≤τ *
τ 
1
*
Qif (t ) = ∑ 2 Perc
(t − τ )  − 2  , τ ≤ τ*
τ * τ * 
τ =1
full, the baseflow can be calculated by setting
(A6)
Sbf(t)=Sbfmax in equation (A5). Equation (A4)
where τ* is the duration of the period after the
reduces so that the water entering the reservoir is
rainstorm until the interflow ceases, Qif(t) is the
equal to what flows out calculated with equation
∗
interflow at a time t, is the effective
(A5). After the base flow reservoir filled, the
percolation on day t-τ. The effective percolation
remaining percolation water fills up the interflow
is defined as the total percolation
flow reservoir started from the hillslopes by
amount needed for refilling the baseflow aquifer.
gravity under these circumstances the flow
Refer to Steenhuis et al, (2009) for more details
decreases linearly (i.e., a zero order reservoir)
on the model development. References are in the
after a recharge event. The total interflow at time
main text
minus the
t can be obtained by superimposing the fluxes for
the individual events,
17