Download Text S1: Models, Climate Change Scenario Linkages, and

Text S1: Models, Climate Change Scenario Linkages, and Parameter Assumptions
S.1 Description of the synthetic streamflow generator
Due to the high seasonality of flows in the Nile Basin, an annual streamflow generation process is
inadequate, so a monthly flow model was developed. Normal and log-normal specifications were
used for the monthly flow distributions. For nodes with highly skewed flows, simple log
transformations were insufficient, and simple transformations were applied:
ln( qk ,adj2 (t ))  ln( qk (t )   k ),
(S1)
where qk, adj was the adjusted inflow value used in the log transformation at node k, and the constant γk
was added to observed net inflows qk for all months t in the data series at inflows into Lakes Victoria,
Kyoga, Albert, Tana and river inflows at Kessie, Atbara, Rahad and Dinder.
Besides exploration of means, standard deviations and skewness statistics for the monthly inflows at
each of the k inflow nodes, the analysis included lag regression modeling aimed at determining the
degree to which flows in the previous j months t-1,…, t-j were useful in predicting flows in month j at
each inflow node k, that is, models were constructed as shown in equation (S2):
q k (t )  1 q k (t  1)  ...   j q k (t  j )  c k , or
ln q k (t )  1 ln q k (t  1)  ...   j ln q k (t  j )  c k , or
(S2)
ln q k (t )   k   1 ln q k (t  1)   k   ...   j ln q k (t  j )   k   c k ,
where the number of lag terms and the choice of the linear or logarithmic model form was made
based on the statistical criteria as described below.
First, both linear and log models were constructed with one, two and three lag terms. Second, the
statistical significance of the lag term coefficients was assessed; models were favored as long as
added lag terms displayed convincing evidence of statistical significance (at better than the ten
percent level). The significance of an added term was deemed to be spurious (due to multicollinearity
with previous lags) if it eliminated the statistical significance of previous lag terms while adding
limited explanatory power to the model (as indicated by the value of the adjusted R2 statistic and the
extent to which estimated coefficients proved unstable). Third, autocorrelation in the model’s error
term was evaluated using the Durbin alternative test and the Breusch-Godfrey test for autocorrelation.
If the Null hypothesis of no autocorrelation could not be rejected, the favored model that satisfied
these criteria was deemed sufficient for use in a synthetic flow generation process. If no model
satisfied this third criterion, the value of including additional lags (beyond three) was investigated.
Table S1 presents a summary of the favored flow distributions and the other characteristics critical for
development of the synthetic prediction model at the 11 inflow nodes. For inflow nodes with mostly
normally distribute monthly inflows (Rahad, Dinder), the linear autocorrelation model was favored;
for inflow nodes with mostly log-normally distributed monthly flows (Kyoga), a logarithmic model
was favored. For nodes having a mixture of normal and log-normal inflows, the favored model was
chosen based on the statistical criteria described in the paragraph above (in practice, the
autocorrelation model with non-log transformed flows performed best for all other nodes except Lake
Tana). As shown in Table S1, most models performed well with fewer than three lags, with the
exception of those for the Torrents, the Sobat River, the inflows between Kessie and the Border node,
and the Dinder River, which had autocorrelated error terms. Only with addition of six or seven lag
terms did these problems dissipate, but this was deemed to be based on statistical chance because a)
the autocorrelation reappeared when additional lags were included beyond those particular ones, and
b) the estimated regression coefficients and their significance proved extremely unstable. As a result,
simple linear models (lag-1 or lag-2 in the case of the Border inflows) were chosen for these nodes.
Table S1. Monthly streamflow statistics and diagnostics a
Inflow
node
Victoria b
Kyoga b
Albert b
Torrents
Sobat
Tana b
Kessie b
Border
Rahad b
Dinder b
Atbara b
a
b
c
d
e
Mean flow (st.
dev.)
Range of means
(in mcm/month)
Favored distribution (months)
Raw
flows
2242
(6365)
[-4288;
12106]
-47
[-467;
306
[-284;
Log
(flow)b
Feb-Apr,
Jul
(544)
229]
(594)
729]
394
(451)
[17;
902]
1107
(708)
[264;
1946]
799
(898)
[80;
2732]
942
(1835)
[12;
5573]
2678
(3136)
[248;
8309]
90
(144)
[0;
369]
227
(404)
[0;
993]
971
(1802)
[1;
5412]
Mar, Apr
# Lags – Yes/No (β)c
Autocorrelation
(Y/N)
(P-value)d
Adj. R2
Log
(flow + γ)b
1
2
3
All other
Yes***
(0.49)
Yes***
(-0.13)
Yes***
(-0.11)
No (0.864)
0.22
All
Yes***
(0.64) e
No
No
No (0.405)
0.40
All other
Yes***
(0.56)
No
No
No (0.153)
0.31
Apr-Jun,
Nov
All other
Yes***
(0.75)
No
No
Yes (0.000)
0.56
Jul, Aug,
Oct-Dec
Jan-Jun,
Sep
Yes***
(0.82)
No
No
Yes (0.000)
0.56
Jan, Apr,
Sep-Nov
All other
Yes***
(1.11) e
Yes***
(-0.53)
No
No (0.232)
0.67
Jan-Mar,
Aug,
Oct - Dec
All other
Yes***
(0.68)
Yes***
(-0.35)
No
No (0.841)
0.34
Yes***
(0.76)
Yes***
(-0.22)
No
Yes (0.000)
0.42
Mar,
Aug-Oct
All other
All other
Jun, Nov,
Dec
Yes***
(1.11)
Yes
(-0.61)
No
No (0.251)
0.67
All other
Jun,
Oct – Dec
Yes***
(0.65)
No
No
Yes (0.000)
0.43
Sep-Dec
All other
Yes***
(0.83)
Yes***
(-0.45)
No
No (0.078)
0.46
Raw flows are non-log transformed inflow data
Log model was applied with γ k added to all monthly flows for these nodes because of negative net inflows in
some months.
Significance of β
*** 1 percent level
** 5 percent level
* 10 percent level
Results of the Breusch-Godfrey LM test for autocorrelation. If Durbin’s alternative test yielded significant
differences, these are highlighted by a # symbol.
A log model was favored for the synthetic streamflow generation procedure; for Kyoga inflows, monthly
flows were approximately log normal in all months; for Lake Tana, some months had normally distributed
flows as indicated, but the log normal autocorrelation model performed better.
The synthetic flow generation equation from Fiering and Jackson [1971] for a multiseason multi-site
(with spatial correlation of random terms preserved across nodes) Markov model with normallydistributed monthly flows at node k can be re-written as:
q k ,i , j   k , j 
 k ( j ) k , j
 k , j 1
(q k ,i , j 1   k , j 1 )  t k ,i , j  k , j (1   k ( j ) 2 ,
2
(S3)
where the only change from the original derivation is that the flows are indexed by k, because the
model is applied to more than one streamflow generation node. In this model, the ρ term represents
the correlation between flows in month j and month j-1 for the length of the historical record, μk,j is
the mean flow at node k in month j, qk,i,j is the simulated flow at node k in year i and month j, tk,i,j is a
randomly generated normally-distributed number with mean 0 and variance 1, and σk,j is the standard
deviation of flows at node k in season j. For the case of log-normally distributed monthly flows,
equation (B.3) remains the same, except that the qk,i,j terms represent the log of simulated flows and
all statistics mentioned above pertain to the log flows rather than the raw flows. When using lognormal flows, then, the numbers in the simulated series are correspond to the log of flows, and must
be exponentiated to yield raw flows for the application at hand.
The models used in this application are somewhat more complicated. The first complication is that
flows in some months are log-normally distributed, and in others they are normally distributed. To
allow for this, the expression in equation (S3) is modified to yield equation (S4) below:
k, j 
 k ( j ) k , j
 k , j 1
if q k , j ~ N[ k , j ,  2 k , j ]
t k ,t 1 ~ N[0,1]
q k ,i , j 
(q k ,i , j 1   k , j 1 )  t k ,i , j  k , j (1   k ( j ) 2
____________________________________________________________


 k ( j ) k , j
expln(  k , j ) 
ln( q k ,i , j 1 )  ln(  k , j 1 )  t k ,i , j  k , j (1   k ( j ) 2 
 k , j 1



(S4)

if ln( q k , j ) ~ N[ k , j ,  2 k , j ].
t k ,t 1 ~ N[0,1]
Thus, in the simulation of synthetic flows, if the flow in month j is log-normally distributed, the flow
in month j-1 must be converted to a log flow, even if the j-1 month’s flow is normally distributed.
The second modification is somewhat more complicated. Because more than one lag was included in
the model for some nodes and the lag regression models with untransformed inflows were generally
favored, it is not sufficient to simply include the first order correlations ρ included in equations (S3)
and (S4). Instead, the regression coefficients β1,…, βL were added as needed. These βL coefficients are
somewhat similar to ρ, except that they refer to the relationship between flows in month j and month
j-l, controlling for the flows in all other months 1,...,L, j ≠ l included in the lag model. The final model
is:
 1 k , j


(q k ,i , j 1   k , j 1 )  ...
 k , j 




k




 L k , j ( q
2 


)

t

(
1


(
j
)
k ,i , j  L
k , j 1
k ,i , j k , j
k


k


if q k , j ~ N[ k , j ,  2 k , j ]
t k ,t 1 ~ N[0,1]
q k ,i , j 
(S5)
______________________________________________________
 1 k , j


exp ln( q k ,i , j 1 )  ln(  k , j 1 )  ...
exp ln(  k , j ) 




k




 L k , j exp ln( q
2 
t 
)

ln(

)

exp
(
1


(
j
)
k ,i , j  l
k , j 1
k

 k ,i , j k , j
 
k






t k ,t 1 ~ N[0,1]


if ln( q k , j ) ~ N[ k , j ,  2 k , j ],
3
where the scaling factor (σk,j/σk) on the regression coefficients is necessary to generate meaningful
sequences since the regression coefficients βl are derived for the general inflow series, in which some
months have higher flow than others. This factor ensures that the model accounts for the difference in
the standard deviation of flow in month j and the average standard deviation for flow in all months on
which the regression model was derived, and is analogous to the scaling factor (σk,j/σk,j-1) used in the
lag-1 autocorrelation model discussed by Fiering and Jackson.
To test the synthetic inflow generation model, 400-year sequences were generated at each of the 11
inflow nodes in the model for comparison with the historical sequence. The statistical properties of
these sequences are summarized in Table S2. Some of the statistics are not precisely maintained,
given the selection of a lognormal distribution. Fiering and Jackson (1971) discuss procedures
sometimes used to allow retention of the statistics of untransformed flows, but these procedures
cannot be applied for the Nile Basin inflow nodes because many sequences are badly skewed.
Table S2. Comparison of statistical properties of synthetic and historical inflow sequences
Inflow
node
Victoria b
Kyoga b
Albert b
Torrents
Sobat
Tana b
Kessie b
Border
Rahad b
Dinder b
Atbara b
Mean historical flow
(st. dev.)
Range of means
(in mcm/month)
2242 (6365)
[-4288;
-47
[-467;
306
[-284;
12106]
Mean synthetic flow (st.
dev.)
Range of means
(in mcm/month)
2269 (6035)
[-4136;
(544)
229]
(594)
729]
-39
[-446;
314
[-266;
12064]
(532)
222]
(569)
748]
394
(451)
427
(615)
[17;
902]
[15;
901]
1107
(708)
1084
(674)
[264;
1946]
[237;
1950]
799
(898)
836
(833)
[80;
2732]
[153;
2727]
942
(1835)
950
(1852)
[12;
5573]
[17;
5732]
2678
(3136)
2659
(3044)
[248;
8309]
[250;
8370]
90
(144)
94
(163)
[0;
369]
[0;
370]
227
(404)
217
(388)
[0;
993]
[0;
1000]
971
(1802)
932
(1649)
[1;
5412]
[1;
5150]
Monthly Lag-1
Correlations a
Historic
Synthetic
0.43
0.47
0.64
0.64
0.56
0.55
0.75
0.53
0.82
0.81
0.63
0.67
0.50
0.48
0.62
0.73
0.71
0.55
0.65
0.63
0.57
0.57
a
The monthly autocorrelation values for synthetic flows for the Border, Torrents and Rahad catchments do not quite agree
with the historical values, due to error autocorrelation problems.
The other diagnostic test involves comparison of the cumulative frequency distribution of flows at the
11 generating nodes with the frequency distribution of flows for the historical series. These
distributions are quite close, and are available in Auxiliary File B.
4
S2 Hydrological Model Calibration
This section describes in detail the calibration of a monthly hydrological routing model created using
the available observed historical series of flows. The approach adopted is similar to that taken by the
authors of the Nile-DST [Yao and Georgakakos, 2003]. There are three major differences between the
mathematical relationships employed in this research and those used by Yao and Georgakakos. First,
this research only used regression approaches rather than regression and neural network models. The
second major difference is that the latter does not include streamflow data for the Blue Nile upstream
of the Border gauging station, since data from the Ethiopian catchment were previously unavailable.
Finally, the Nile-DST uses 10-day flows, whereas this research uses a monthly time step. This choice
is purely practical and based on the greater availability of monthly flow data in the Blue Nile and at
various other locations in the basin. It does, however, require the estimation of different regression
relationships (more information on these relationships is available In Auxiliary File C).
The model (hereafter referred to as simmodel) spans from the outlet of Lake Victoria on the White
Nile and Lake Tana on the Blue Nile, to the Aswan High Dam Reservoir in Egypt. It relies on a
combination of level pool models based on conservation of mass principles for reservoirs and some
intermediate river nodes, and empirically-derived regression models for the river nodes where flow is
more complicated. The nodes in the model are shown in Figure S1. Table S3 presents a summary of
the performance of the monthly regression routing model in comparison with historical flow data and
the Nile-DST, and describes known data gaps and/or problems in the model.
Lake
Nasser
Dongola
Merowe
Inflow
Atbara
Atbara
Model Node
Hassanb
Inflow
Tamaniat
Inflow
Tekeze
Khasm el
Girba
TK-5
Inflow Inflow
Rahad Dinder
Inflow
Girba
Net inflow
Tana
Khartoum
Roseires
Lake
Gebel Aulia
Potential
Reservoir
Existing
Reservoir
Sennar
El Deim
Melut
Sudd exit Inflow
Inflow
Mandaya
Sobat
Inflow
Torrents
Mongala
Pakwatch /
Panyango
Net inflow
Albert
Lake
Albert Albert
Inflow
Karadobi
Lake
Tana
Bahir Dahr /
Tana Outlet
Karadobi Kessie
Mandaya
Border
Malakal
Loss
Sudd
Inflow
Border
Paraa /
Kyoga
Outlet
Lake
Net inflow
Kyoga
Kyoga
Inlet
Kyoga
Inlet
Owen Falls/
Victoria Outlet
Lake
Victoria
Net inflow
Victoria
Figure S1. Simmodel schematic, showing system inflow, routing and reservoir nodes.
5
Table S3. Diagnostics of outflows of hydrological simulation model
Simmodel Correlations
11.3
(360)
26.4
(276)
83.8
(276)
70.0
(334)
125.4
(792)
DST
(#
months)
145.6
(360)
33.2
(276)
159
(276)
140.2
(334)
390.4
(780)
154.8
(851)
154.8
(768)
110.5
(845)
22.4
(120)
207.3
(833)
7.6
(48)
0.860
10.5
(252)
No
overlap
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
Historical
flow
DST
simulation
Victoria
0.985
0.994
Kyoga
0.980
0.995
Albert outlet:
Pakwatch/ Panyango
0.957
0.992
Torrents
0.965
0.991
Mongalla
0.948
0.966
Sudd Exit
0.659
0.811
Malakal
0.913
0.980
Melut
0.851
0.970
Gebel el Aulia
0.806
Node in system
Lake Tana
Kessie
Guder @ Karadobi site
Mendaya site
Elevation:
0.992
1.000
N/A
N/A
Sum of squared errors
(relative to historical
series)
Simmodel
(# months)
Border
0.981
0.990
N/A
N/A
El Deim a
1.000
1.000
N/A
N/A
Roseires inflow
0.994
1.000
111.1
(768)
N/A
N/A
0.985
332.6
(1097)
N/A
Inflow:
0.986
Outflow:
0.978
589.3
(636)
850.6
(624)
Khartoum – Blue Nile b
0.969
0.982
512.6
(140)
Tamaniat b
0.961
N/A
Hassanb b
0.963
N/A
512.9
(154)
2651.2
(947)
2622.5
(947)
Khasm el Girba
1.000
0.978
N/A
N/A
Atbara
0.996
0.974
31.0
(785)
153.5
(522)
Dongola – Entrance to
HAD c
0.973
0.979
2858.2
(840)
3340.7
(768)
Roseires outflow
Sennar b
6
Known problems
Based on post Owen Falls elevation-discharge
curve
Elevation-discharge curve is inaccurate for
high lake stands; Pakwatch gauge unstable.
Underprediction of flow during high flow
years, probably due to unknown local rainfall
contributions; DST displays similar problems
Underprediction persists, but Sobat inflows
mask problems
Underprediction persists, short historical flow
sequence
Short flow sequence, precise operating rules
may not be accurate, monthly model does not
explain backwater effects adequately
Natural outflow data is inconsistent with
elevation-discharge relationship
Local inflow derived from historical flow data
No stream gauges available, no DST modeling
No stream gauges available, no DST modeling
When possible, local inflow derived from flow
at El Deim, which is more reliable.
Some notable inconsistencies with Border
gauge and Roseires late in the series
Correlation with historical flows to 1964;
beginning of regulation at Roseires began
then; assumes constant irrigation demand
Correlation with historical flows to 1925;
before regulation began.
N/A
N/A
Local inflow derived from historical flow data
at Girba.
Correlation up to 1966, at which point
regulation of flows at the High Aswan Dam
began.
S3 Details on the Climate Scenario
This paper reports on the economic performance of the Blue Nile infrastructure under conditions
corresponding to the Intergovernmental Panel on Climate Change’s A2 scenario. This scenario was
constructed using downscaled projections for 2050 from three models from the IPCC reports: PCM,
CSIRO and HADCM3. The GCM projections were further processed using the WATBAL rainfall-runoff
model developed by Yates [1996] to yield runoff. The results reported here correspond to the three-model
ensemble mean. Ensemble means are one approach for conducting hydrological impacts assessment
[IPCC, 2007]. In general, the A2 scenario projections suggest increased temperature, slight but spatially
variable increases in precipitation, and more variable decreases in runoff (due to increased potential
evapotranspiration), over much of the Nile basin (Table S4).
Table S4. Summary of Three-Model Mean Projections for 2050, from Alyssa McCluskey; Model Range in Brackets.
ΔPrecipitation
ΔRunoff
(% Change over historical)
(% Change over historical)
A2
B2
A2
B2
6.8
6.3
-6.8
-7.4
Atbara
[1.1–11.2]
[0.5–11.2]
[(-16.6)–(-0.8)]
[(-17.1)–2.5]
1.7
1.5
-7.7
-7.7
Karadobi
[(-5.0)–5.3]
[(-4.4)–5.9]
[(-16.4)–(-3.0)]
[(-17.1)–(-1.5)]
1.4
0.8
-5.1
-6.2
Mabil
[(-2.5)–6.0]
[(-3.4)–5.3]
[(-10.5)–(-0.1)]
[(-11.8)–(-1.5)]
2.8
1.9
-0.9
-2.5
Mendaya
[0.4–6.9]
[(-1.3)–6.7]
[(-3.6)–3.1]
[(-6.1)–(2.5)]
3.0
3.3
-3.5
-3.7
Border
[(-2.8)–8.6]
[(-3.7)–7.4]
[(-10.1)–2.2]
[(-11.9)–0.4]
1.9
3.6
-36.1
-41.4
Dinder / Rahad
[(-6.8)–9.0]
[(-6.7)–9.2]
[(-50.9)–(-20.1)]
[(-50.0)–(-36.2)]
1.9
1.6
-4.9
-5.6
All Blue Nile
[(-2.8)–6.5]
[(-2.4)–4.2]
[(-11.1)–(-0.6)]
[(-12.5)–(-1.9)]
7.0
5.9
-2.0
-2.8
Baro-Akobo
[1.2–10.7]
[(-2.0)–10.7]
[(-8.2)–3.4]
[(-13.1)–6.8]
58.8
59.5
0.1
66.8
Main Nile a
[35.4–102.4]
[36.7–102.4]
[0.1–0.1]
[0.1–200.0]
6.5
5.5
-4.5
-6.4
All Nile
[2.6–8.7]
[0.0–8.7]
[(-9.3)–(-0.8)]
[(-13.4)–(-0.8)]
The Parallel Climate Model (USA) model predicts very large increases in rainfall and runoff for the Main Nile on
a percentage basis, but the magnitude of these increases is less dramatic since that river reach passes through arid
desert.
Sub-basin / catchment
a
The analysis of sensitivity to inflows was informed by a careful reading of the literature on Nile Basin
projections. Indeed, there are a growing number of climate projections – published and unpublished – for
the Nile system (see Table S5). These have in the past been used primarily to study potential impacts on
the system; there do not appear to be any specific planning applications that use them. The range of
projections is extremely large, and this range must be interpreted with caution given the problems with
using GCMs for hydrological application. Adopting a multi-model ensemble mean approach, the range
shrinks considerably. For temperature, 2-3°C increases appear reasonable by 2050 over most of the Nile
Basin; for precipitation, mean changes are slightly positive, and finally runoff is expected to decrease
somewhat. These projections are used to inform the construction of the sensitivity analyses of inflows for
the planning application of this research, which go from basin-wide decreases of 15% to increases of 6%.
Table S5. Summary of Studies of Historical Climate Trends and Future Projections
7
Source
Analysis
Elshamy et al., 2000
TAR Projections
(2050)
Conway, 2000
Hulme et al., 2001
Historical trends
Historical trends
(20th Century)
Nyssen et al., 2004
Historical trends
Sayed & Nour, 2006
TAR Projections
SNC-Lavalin, 2006
TAR Projections for
A1B (2050)
IPCC, 2007
AR4 Projections
Conway et al., 2007
AR4 Projections for
A2, B1 (2050)
Beyene et al., 2007
AR4 Projections
(Three periods)
Elshamy et al., 2008
AR4 Projections for
A1B (2081-2099)
McCluskey, 2008
TAR Projections for
A2, B2 (2050, 2080)
Summary
2-4.3°C increase over Nile Basin; 3-4°C increase in
Northern Sudan and Egypt
-22 to +18% change in precipitation
No precipitation trend over Blue Nile
0.5°C increase in Africa, 0.6°C in Ethiopia
No precipitation trend over highlands in Ethiopia /
Eritrea
-2 to +11% change in Blue Nile Basin precipitation;
-1 to +10% change in White Nile Basin precipitation
-14 to + 32% inflows to Lake Nasser
+7.4% mean increase in precipitation in Equatorial
Lakes (Range: +4.3 to 14.2%)
+23% change in inflows to Southern Nile (Range: +4
to 37%)
Increased rainfall over Nile Equatorial Lakes Region,
GCMs inconsistent over Ethiopia and Sahel
+2.2°C mean increase in Ethiopia (Range: +1.4 to 2.9)
+1 to 6% mean increase in precipitation in Ethiopia
Mean precipitation: +15% (2010-2039); -2% (20402069); -7% (2070-2099)
Inflows at Aswan: -16% (2070-2099)
2-5°C increase over Nile Basin
+2.4% change in precipitation (Range: -15 to +14%)
+2-14% increase in potential evapotranspiration
-15% mean change in runoff (Range: -60 to +40%)
Slight mean increases in precipitation; decreases in
runoff
S4 Modeled Climate Change Linkages
The specific climate linkages included in this research are: a) changes in runoff; b) change in net
evaporation over reservoirs; c) changes in hydrological routing relationships; d) increases in crop-water
requirements due to temperature increases; e) inclusion of the value for carbon offsets from hydropower;
and f) increases in the value of hydropower and water due to increasing scarcity of these outputs.
a. Runoff. To obtain the A2 scenario changes in inflows, local inflows in the Nile sub-catchments were
perturbed by the predicted changes shown in Table S1. Because the runoff projections found in the Nile
climate change literature span a larger range, as summarized above, these projections were supplemented
with sensitivity analyses on inflow changes (ranging from -15% to +6% over the entire Nile system).
b. Net evaporation. Changes in net evaporation from system reservoirs were modeled to include the
effects of rising temperatures and perturbations in average precipitation over the water surface. To
calculate evaporation changes, an energy balance approach was used [Maidment, 1993]:
E p  Fp1 A  Fp2 D, where
(S6)
Ep = rate of open water evaporation (mm/day);
A = net radiation (Rn) + advected energy (Ah) = energy available for evaporation (mm/day);
8
D = average vapor-pressure deficit (in kPa);
Fp1 = coefficient that is a function of temperature and elevation of the site; and
Fp2 = coefficient that is a function of temperature, wind speed, and elevation of the site.
All other things equal, an increase in temperature leads to higher Ep, and the change in Ep can be written
and calculated as ΔEp(ΔT).1 This change (converted to mm for month t to yield ΔEp,t (T)) was then added
to the change in the historical mean of precipitation (in mm/month) to obtain the change in net
evaporation:
NEt  E p , t (T )  d  Pt , where
(S7)
ΔNEt = change in net evaporation in month t (mm/month);
ΔPt = change in average precipitation in month t (mm/month)
d
= days in month t.
c. Hydrological routing. One serious problem with hydrological analysis under climate change conditions
is the possibility of large-scale changes affecting the calibrations of routing models. In particular, for the
Nile system, White Nile flow upstream of Khartoum through central Sudan is highly complex. Existing
models represent this as a function of river stage and the time of year, both of which influence backwater
effects from the Blue Nile confluence. The model used in this research also includes a switching
regression model to better predict losses in the Sudd during high and low flow periods.2
d. Crop-water demands. Using an agronomic approach, changes in the demand for irrigation water due to
climatic influences were obtained using the Penman-Monteith procedure for calculating the reference
crop evapotranspiration ET0 [Adams et al., 1998; Allen et al., 1998; FAO, 1992]. ET0, when multiplied by
the appropriate crop coefficient Kc,i, yields the crop water requirement for crop i. The Penman-Monteith
Equation is:
900
u 2 (e s  e a )
T  273
ET0 
, where
   (1  0.34u 2 )
ET0 = reference crop evapotranspiration (mm/day);
Δ
= slope of the vapor pressure curve (kPa/°C);
Rn
= net radiation (MJ/m2-day);
G
= soil heat flux (MJ/m2-day), usually assumed to be zero;
T
= monthly mean temperature (°C) ;
u2
= wind speed at 2m height (m/s);
es-ea = Vapor pressure deficit (kPa); and
γ
= psychrometric constant (kPa/°C).
0.408 ( Rn  G)  
(S8)
Changes in ET0 due to mean temperature changes can be calculated using Equation 7 evaluated at the
original and new mean temperatures. If one assumes that irrigators use water efficiently and do not alter
1
Determining the change in open water evaporation that will result from climate change is in reality much more
complicated than this. Other climate factors (humidity, wind speed) that influence the energy available for
evaporation and the coefficients Fp1 and Fp2 will most likely also change. However, the accuracy of GCM and RCM
predictions of these factors is typically not easy to assess; as a result they are not explicitly discussed here. A more
complete model could include these factors.
2
More details on the calibration of this model follow.
9
cropping patterns in response to climate, these calculated changes in ET0 can be applied to scale water
demands. Note that these changes probably overstate water demand increases (and may therefore
overstate the risk of deficits): Ricardian studies that account for farmer crop choices and adaptation argue
that farmers will switch to less water-intensive crops as temperature increases [Kurukulasuriya, 2006;
Mendelsohn and Dinar, 1999].
e. Carbon offsets. The value of carbon offsets vo,i for year i was obtained by multiplying the net offsets Oi
(in tons of CO2) by the value of offsets in year i (US$/ton CO2 offsets in year i), which is a function of the
unit cost of offsets in year 1 (co,1; US$/ton CO2 offsets in year 1) and the relative change in the value of
offsets over time (Δvo; in constant %/year):
vo,i  Oi  co,1  (1  vo ) i 1 .
(S9)
We assumed that the value of offsets will increase over time (Δvo = 0.5%/yr; range 0-1.5%/yr), as
greenhouse gas emissions controls become tighter.
f. Economic value of system outputs. The relative changes in the value of energy and water were modeled
with a similar constant annual percent change. In a climate change world, we feel that it is safe to assume
that the value of energy will increase as temperatures go up, reflecting lower supply of conventional
greenhouse-emitting sources, and higher demand for cooling energy and due to gradual economic
development. Similarly, we believe that the value of water in the Nile basin under historical flow
conditions will increase over time because there is no more free water in the Nile basin. Under climate
change, for scenarios that include reduced inflows, we believe this relative value will increase more
quickly, but for the analyses with increased runoff, we expect the increase to be slower.
S5 Details of Project Costs and Benefits3
Costs. A large dam in the Blue Nile gorge would require a capital investment of somewhere around
US$2.75 billion; another US$800 million would be required to provide the necessary interconnection of
transmission lines from the dam to regional power markets (mostly in Egypt). These capital costs were
calculated using a fairly detailed costing-up approach based on the costs of the various dam components
(the total costs are allowed to vary by +/- 20% in the economic simulations). Because the dams are to be
built using roller compacted concrete, it is possible that filling and operation of the dam could begin
before all works are complete (estimated to take 10 +/- 2 years, based on a proposed timeline for
construction). Electrical infrastructures are assumed to be replaced every 20 years; civil works are
allowed to last over the assumed 75-year project time horizon (range 30-100 yrs). Routine maintenance is
assumed to be 50% of annualized capital costs (+/-15%).
These are the costs that the project studies include, but a large dam in the Blue Nile canyon would also
have a number of other economic consequences: carbon emissions during construction, resettlement and
economic compensation for lost livelihoods, possible increased downstream irrigation deficits in some
locations and in some years, as well as decreases in hydropower production at downstream dams, and the
costs of possible catastrophic dam failure. First, carbon emissions would result from construction and
decomposition of biomass in the flooded reservoir area; these are estimated to be 6.4 million tons of CO2
based on project documents (range 4.8-8.6). These carbon emissions are valued at a cost of US$20/ton
($10-30/ton). Second, there are actually few households living in the Blue Nile canyon; environmental
and social impact studies suggest that about 120 households would be affected (60-340). The effect on
grazing and agricultural lands would be more substantial. A number of farmers rely on the annual Blue
3
Unless otherwise noted, these data come from unpublished project planning documents.
10
Nile flood to implement small-scale irrigation as the flood recedes. Project documents estimate that some
10000 hectares are exploited in this way in downstream Sudan and Ethiopia and yield total economic
rents of US$1.5 million, with grazing occurring on another 15000 or so hectares (for an annual economic
value of US$1 million). These numbers would obviously vary depending on how far downstream on the
Blue Nile a new dam is placed. For simplicity, we represent it by two parameters in our model: total area
lost (25000 hectares +/-50%) and the cost of rehabilitation for small pumping schemes in affected areas
(US$20; range 10-100). It is important to note that lack of such compensation for affected people could
result in higher damages.
Third, downstream increases in deficits and decreases in hydropower production are obtained directly
from the hydrological model. The value of water in irrigation is assumed to be US$0.075/m3 (we use a
large range due to the extreme uncertainty associated with this parameter: 0.03 – 0.15), and damages
associated with deficits are assumed to be 2 times this amount (range 1-3), due to the added possible loss
of complementary production inputs such as fertilizer, labor, etc.4 Hydropower is valued at
US$0.065/kW-hr (Range: 0.04 – 0.09), based on the cost of alternative supplies (mainly natural gas in
Egypt). Finally, we represent catastrophic failure as a random event that occurs with an independent
annual probability of 0.01% (range 0.002 – 0.02%). If a failure occurs, the economic damage is computed
as the cost of reconstruction of the dam plus the sum of all lost benefits during the period of
reconstruction (monetizing catastrophic flood damages beyond this lower bound cost warrants further
study).
Benefits. On the benefits side of the ledger are: the production benefits from increases in system outputs
(hydropower at the dam and downstream, irrigation water downstream), flood control, and carbon offsets
from hydropower. The physical quantities of these outputs are largely obtained from the hydrological
model and are discussed in more detail in the results section. The value of hydropower and water are
taken as specified above (US$0.065/kW-hr, range: 0.04 – 0.09 and US$0.075/m3, range: 0.015 – 0.15).
Flood control benefits are very difficult to estimate using a monthly hydrological model, in this analysis
these are calculated as the reduction in the maximum monthly flow in each year – from the hydrological
model – multiplied by expected annual flood damages (US$8.8 million/annum, range 4.4-17.6). Finally,
carbon offsets are multiplied by an offset factor based on the average emissions of alternative power
generation in Egypt (0.52; range 0.3 – 0.6), which comes from a variety of sources including combined
natural gas turbines and hydropower. These offsets are valued at the same amount as the construction
emissions (US$20/ton; range 10-30).
Finally, the real value of irrigation water, offsets, and hydropower is allowed to change over time based
on the climate scenario being evaluated. In a world with climate change, it seems reasonable to expect
that the value of energy will increase as temperatures go up, reflecting both cutbacks in the supply of
conventional greenhouse-emitting sources due to climate change mitigation, and higher demand for
energy for cooling and due to gradual economic development (average real change = 0.5%/yr; range 01.5%). This is in contrast to the no climate-change condition, in which pressures on the value of energy
would probably be lower (average = 0%/yr; range of -0.5 to +0.5%/yr). In contrast, it is probably
reasonable to expect that the value of water in the Nile basin will increase over time even if historical
climate is maintained (average 0.5%/yr, range 0-1%); there is ample evidence that there is no more free
water in the Nile basin even as consumptive uses continue to increase [Waterbury and Whittington, 1998].
Under climate change, for the A2 and sensitivity scenarios that include reduced inflows, this trend is
4
We note that these are perfectly correlated in the model; in other words, if the value of timely water is US$0.15/m3,
then the cost of added deficits is also at the upper end of its range: US$0.3/m3.
11
likely to accelerate (an average change of 1%/yr is assumed; range 0.5-1.5%). However, for the
sensitivity analyses with increased runoff, this change is decreased to 0%/yr (range -0.5 to +0.5%/yr).5
Several potential economic impacts are not included in this application. First, there are no existing plans
to use the proposed dam for irrigation or municipal water supply. In addition, recreation, navigation,
fisheries and public health implications are not included because the Blue Nile canyon is very sparsely
populated and these impacts are expected to be minor. Nonetheless, a more complete assessment of these
would be warranted before any large projects are carried out. In contrast, some costs and benefits shown
in Table 1 may be substantial but data are lacking at this time to properly assess them: a) effects of
sediment at the dams and downstream, b) changes in environmental and ecosystem services, and c)
secondary impacts. With regards to sediment, a large dam would have sufficient dead storage to avoid
siltation problems over at least 75-100 years. The dam would also substantially decrease sediment flows
downstream, providing benefits for Sudanese dam operation but perhaps negatively affecting farmers
engaging in recessional irrigation. For ecosystem impacts, preliminary environmental impact assessments
of the dam site did not identify critical negative ecological issues. Finally, secondary and economy-wide
impacts – such as enhanced regional economic integration, peace and cooperation, and general
development impacts – are not included; these may be substantial but can be difficult to attribute to
specific projects and require additional research with general equilibrium tools [Bhatia et al., 2005;
Boardman et al., 2005; Whittington, 2004; Whittington et al., 2009].
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5
There is obviously a high degree of uncertainty surrounding these relative price changes, but these have been
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12
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13