el nifio and the natural variability in the flow of the nile river
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WATER RESOURCES RESEARCH, VOL. 32, NO. 1, PAGES 131-137, JANUARY 1996
El Nifio and the natural variability in the flow of the Nile River
Elfatih A. B. Eltahir
Ralph M. Parsons aboratory,Departmentof Civil and Environmental ngineering
Massachusettsnstitute of Technology,Cambridge
Abstract. Natural variability n the annual low of the Nile River hasbeen the subjectof
great nterest o the civilizationshat havehistorically ccupiedhe banksof that river.
Here we report results rom analysis n two extensive ata setsdescribing easurface
temperature f the PacificOcean,and the flow of water n the Nile River. The analysis
suggestshat 25% of the natural ariabilityn the annual lowof the Nile is associated
with E1 Nifio oscillations. procedures developedor using his observed orrelation o
improve he predictability f the Nile flood.A simplehypothesiss presentedo explain
physicallyhe occurrence f the Hurst phenomenonn the Nile flow.
Introduction
The stories n the Bible and the Koran concerning rophet
Joseph nd he Pharaohof Egyptpoint,amongother hings, o
the importance f the Nile water o the ancient ivilizations f
Egypt (the subjectof thesestories s a predictionabout he
occurrence f a periodwith food surplus ollowedby a famine
episoden Egypt). n recenthistory, he High AswanDam was
constructed to control the annual flow of the Nile and to
protect he regionagainst roughts nd loods. he hugestruc-
ture of the dam standsas a witness o the desperateeffortsby
man to control he naturalvariabilityof thisvital resource.Any
reduction n the uncertaintyabout the Nile flood would rep-
resent a valuable contribution o water resourcesmanagement
in Egypt.This is particularly rue given he naturaland social
Conditionsn this arid region,where water is by far the most
importantnatural esource, ndwhere he currentpopulation
problemwill increase he demandon water beyond he gener-
ous supplyof the Nile.
Recent studies e.g.,Ropelewskind Halpert, 1987;Simpson
et al., 1993] ndicatehat oscillationsn the stateof the ocean-
atmosphere ystemn the Pacific egion are related to inter-
annual fluctuationsof rainfall and river flow in several egions
of the world. These oscillations are known as E1 Nifio-
SouthernOscillationsENSO). The earlypaperof Bliss 192•]
lists he Nile flood as one of 10 geophysical ariables hat are
related to a Southern Oscillation index. The recent study of
Quinn [1992]explores he useof the historical ecordof max-
imum Nile flood to extend the records of the Southern Oscil-
lation index. In a recent paper, Moss e al. [1994] use the
SouthernOscillation ndexas a predictorof the probabilityof
low streamflows n New Zealand. In this study, we test the
hypothesishat he natural ariabilityn annual lowof the Nile
River at Aswan is related to ENSO and that such information
canbe used or improvinghe predictability f the Nile flood.
Finally,a simplehypothesisspresentedo explain omeof the
statistical characteristics observed in the time series of Nile
flow; n particular,we proposehat the relationbetweenENSO
and the Nile flood may explain the Hurst phenomenon: he
mean of the annual flow process n the Nile River varies n
time following ENSO, resulting n a non-stationaryprocess,
Copyright 996by the AmericanGeophysical nion.
Paper number 95WR02%8.
0043-1 $ 97/%/95WR-02%8505.00
and causinghe Hurst phenomenonthe term nonstationarys
used to indicate that the mean of the process s a variable
functionof absolute ime).
Data
The data used n this analysis onsistof annual flow in the
Nile River at Aswan for the century hat extendsbetween the
years1872and 1972.The monthlydistribution f the Nile flow
is described y Figure 1, which shows he long-term average
flow for each month. The annual flow of the Nile (the Nile
flood) s defined s he cumulativelowmeasuredromJuneof
anyyear to May of the followingyear. A typicalmonthly low
in the Nile for any year followscloselya seasonal ycle,with
one peak and a long recession. ence most of the natural
variability n the Nile flow s capturedby the annual low. The
measured low of the Nile has been naturalizedby removing
anthropogenicrends,but the findingsof this paper are not
sensitive to this correction. This data set on the Nile flow has
been suppliedby the Ministry of Water Resources f Egypt.
The index of ENSO used in this study is a homogenized
monthlyseriesof the mean sea surface emperature SST)
anomalyaveragedover the regions6ø-2øN,170ø-90øW; øN
6øS, 180ø-90øW;and 6ø-10øS, 150ø-110øWduring the same
time period,1872-1972.This ndexof ENSO waspublished y
Wright 1989].
Relation Between ENSO and the Nile Flood
The natural series of annual flow of the Nile at Aswan is
shown n Figure 2. The yearswith E1 Nifio eventsare defined
according o the classification f Rasmusson nd Carpenter
[1983] and are marked n Figure 2 with solid circles.From
Figure 2 we may conclude hat ENSO eventsare associated
with thoseyearswhen the flow of the Nile is low compared o
the long-term average.This observationprompted a more
careful look at the correlations of ENSO indices and the Nile
flow. The indexof ENSO is averagedover four quartersof the
year: December,January,and February;March, April, and
May; June, July, and August;September,October, and No-
vember. Then the correlations between the annual flow of the
Nile (the flow from June to May) and the average ndex of
ENSO for eachof thesequarters re computed. he different
quarters re denotedby negative positive) ignwhen he cor-
relation s computed etween he Nile flood and SST in the
131
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132 ELTAHIR: NATURAL VARIABILITY IN FLOW OF THE NILE RIVER
2O
• lO
Jun Sep Dec Mar
Figure 1. Seasonalcycle of the Nile flow at Aswan.
preceding succeeding) ear. The correlationcoefficients re
shown Table 1. The correlation between the Nile flow and
ENSO index averaged or the monthsof September,October,
and November s about 0.5. The corresponding ercentageof
the variance n annual flow explainedby the ENSO index is
25%. The scatterplot for this relation is shown n Figure 3.
An explanation s provided or the relation betweenENSO
and the annual flow of the Nile based on observed correlations
in the globaldistribution f sea evelpressure.n particular,we
note the observedpositive correlation between the annual
mean sea level pressureat the sourcesof the Nile, in the
Ethiopian Plateau, and the annual pressureat Darwin, Aus-
tralia [seeTrenberth nd Shea,1987].A positive nomaly n the
annualsurfacepressure t Darwin is an indicatorof the onset
140
120
'• 40
0 i I I I I i i i i i
1870 1890 1910 1930 1950 1970
years
Figure 2. Annual fluctuationsof the "natural" flow in the
Nile at Aswan for the years 1872-1972. E1 Nifio events are
marked with solid circles.
of an ENSO event.But according o the observations, arwin
pressure s positivelycorrelatedwith pressureanomaliesover
the Ethiopian Plateau. The laws of atmosphericdynamics e-
quire that a positiveanomaly n annualsea evel pressure ver
the Ethiopian Plateau is associatedwith decreasedconver-
genceof atmosphericmoistureand therefore ess ainfall. The
observational tudy of Janowiak [1988] confirms hat ENSO
events are associated with drier than normal levels of summer
rainfall in a region that includes he Ethiopian Plateau. This
reduction n rainfall causes negativeanomaly n the annual
flow of the Blue Nile. The latter contributes most of the inter-
annual variability n the Nile flow.
ENSO and Predictability of the Nile Flood
The observed correlation between ENSO and the flow in the
Nile has important implicationson the predictabilityof the
annual low n the river.A simpleprobability able s developed
for use n predictions f the Nile flood. This table s basedon
the classificationhat is describedn Figure 4 and Table 2. An
average lood is defined as the annual flow that has a magni-
tudebetween 0 and100km . The ong-termverageor the
Table 1. Coefficients of Correlation Between the Annual
Flow of the Nile and the Index of ENSO Averaged or
Different Quarters of the Year
Coefficient of
Quarter of the Year Correlation
Sept.,- Oct.,- Nov.- -0.15
Dec.,- Jan., Feb. -0.20
March, April, May -0.36
June,July,Aug. -0.45
Sept.,Oct., Nov. -0.50
Dec., Jan., Feb.+ -0.49
March, April,+ May+ -0.42
June, July, Aug.+ -0.06
A negative positive)sign ollowingany month indicates hat the
correlation s performedbetween he Nile flood and SST in the year
preceding following) he peak of the Nile's flow.
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ELTAHIR: NATURAL VARIABILITY IN FLOW OF THE NILE RIVER 133
140
120
100
80
so
40
2O
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
SST index of ENSO in øC
Figure 3. Scatterplot of the data showinghe relationbetween he annual low of the Nile and the indexof
ENSO or themonthsf September,ctober,ndNovember,or theyears 872-1972.hecoefficientf
correlation s -0.5. The straight ine is the regressionine.
Nile flood sabout 0 km . f theannuallow s arger han100
km , t is classifiedshigh. f the same low s smallerhan80
km3, then t is classifieds ow.The dataon SSTare classified
similarly nto cold, normal, and warm conditions. he bound-
aries between these three conditions are temperatures of
-0.5øC and 0.5øC, espectively. he choices f the boundaries
between the different conditions for SST as well as the Nile
flood are subjective. ndeed, the same exercisecan be per-
formed using any alternative easonable hoices.Table 2 de-
scribes he prediction probabilities or the Nile flood. This
140
120
100
80
40
2O
[17}
• [17)
(1)
I I
[6)
(11)
I
I ,I
(2)
(14)
-2 -1.5 -1 -0.5 0 0.5 I i .5 2
SST index of ENSO in øC
Figure 4. Categories f the Nile flood and ENSO index.The numberof data points n eachgroup s also
shown.
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134 ELTAHIR: NATURAL VARIABILITY IN FLOW OF THE NILE RIVER
Table 2. Conditional Probabilityof the Nile Flood Given
the SST Index of ENSO Based on Observations of
1872-1972
Flow
SST Low Average High
Cold 0.02 0.49 0.49
Normal 0.27 0.58 0.15
Warm 0.58 0.34 0.08
table consists f the conditionalprobabilityof having a Nile
flood in a certain category low, average,or high) given a
certain observedSST condition cold, normal, or warm). For
example, he probabilityof havinga low flood givena cold SST
condition s 2%; and the probabilityof having a high flood
givena warm SST conditionss 8%. In order to appreciate he
information content in the relation of ENSO and the Nile
flood, we note that in absenceof any informationabout SST,
the probabilityof havinga low flood n anyyear s 26%, and the
correspondingprobability for having a high flood is 25%.
These estimates re basedsolelyon the past recordsof Nile
floods.Hence knowledge f SST conditions ouldpotentially
be very useful n predictionof the Nile flood.
Recent studiespresentedoptimisticconclusions bout the
predictabilityof ENSO events, suggestinghat these events
could be accurately redicted 1 or 2 yearsahead usinga cou-
pled model of the ocean-atmosphereystem see Cane et al.,
1986]. n this study,we utilize predictions f SST n the Pacific
Ocean,whichare obtainedusinga coupledocean-atmosphere
model, for the purposeof makingpredictions bout the Nile
flow. The predictions f SST are obtainedusingan improved
versionof the model describedby Cane et al. [1986]. These
predictions re issued months n advance nd were supplied
to us by Stephen E. Zebiak of Lamont-Doherty Geological
Observatory f Columbia University.Table 3 showspredic-
tions of the SST indexof ENSO for the years1973-1989. These
predictions re used o make similarpredictions or the Nile
flood in the sameyears.These flood predictions re made as
early as the February hat precedes he Nile flood of interest.
The observed loods or the sameyears are shown n Table 2
for verification urposes.n 12 of the 17 years he prediction f
the most probable lood matches he observations:or exam-
ple, the prediction or the mostprobable lood or 1984 s a low
flood evel hat matcheshe observationor that year.Since he
autocorrelationoefficientt lag1 in theNile lood eriess
insignificant---0.22), here s very ittle persistencehat canbe
used or forecasting urposes.Hence in absence f any infor-
mation aboutSST, the predictionof the mostprobable lood
for anyof the yearswill be the average lood.According o the
observationsor1973-1989,his redictionatchesheobser-
vations n 9 out of the 17 years.From this comparison, e
concludehat the useof ENSO predictions ould mprove he
Nile flood predictions ignificantly.
The value of the probability able for predictionpurposes
can be further appreciated y consideringhe extrem flood
conditions. predictionof a warm SST translatesnto a very
lowprobability8%)ofhaving high lood.On heother and,
a prediction of a cold SST translates nto an even smaller
probability 2%) of havinga low flood. It is encouraginghat
for the years1973-1989,none of the yearshad cold SST/low
floodor a warmSST/highloodconditions. or the purpose f
water resourcesmanagement,he ability to (almost) ule out
the possibility f occurrencef a high lood or a low lood),9
months ahead, could be of great economicvalue.
ENSO and the Hurst Phenomenon
Hurst [1951] observed hat the time seriesof annual low in
the Nile River exhibits statistical characteristics that are not
compatiblewith a seriesof purelyrandom luctuations: urst
phenomenon. his observations most relevant o the hydro-
logicdesign f interannual torage eservoirs. or example,he
sizeof a reservoir n the Nile Riv r, whichon average,ails
once every n years n supplyingexactly he long-term mean
flow, s roughly roportionalo I/ø'72 In contrast,or any
purely random river flow the same reservoirsize s propor-
tionalono.s.Henceorany pecificesignriteria, reservoir
on the Nile has to be of a relatively arge size.
Table 3. Predictions of SST and Predictions and Observations of the Nile Flood 1973-1989
Predicted SST
Predictions f Flood Probability),
% Observed Flood
Year øC Category Low Average High km Category
1973 -0.6 cold 2 49 49 83 average
1974 -0.6 cold 2 49 49 90 average
1975 -0.1 normal 27 58 15 102 high
1976 0.9 warm 58 34 8 80 average
1977 1.3 warm 58 34 8 92 average
1978 - 0.3 normal 27 58 15 86 average
1979 0.0 normal 27 58 15 69 low
1980 -0.3 normal 27 58 15 82 average
1981 0.0 normal 27 58 15 85 average
1982 2.5 warm 58 34 8 69 low
1983 2.1 warm 58 34 8 72 low
1984 1.7 warm 58 34 8 53 low
1985 0.5 normal 27 58 15 82 average
1986 1.0 warm 58 34 8 73 low
1987 1.9 warm 58 34 8 68 low
1988 0.2 norm l 27 58 15 115 high
1989 0.4 normal 27 58 15 81 average
The flood predictions re described y the probabilities f havinga certain lood evel.
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ELTAHIR: NATURAL VARIABILITY IN FLOW OF THE NILE RIVER 135
lOO
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
SST index of ENSO in øC
Figure 5. The relationbetweenENSO indexand the varyingmean of the annual low n the Nile River. The
annual low of the Nile is averaged ver a smallwindowof ENSO indices, achwith a width of 0.5øCcentered
around -1.5 ø, -1.0 ø, -0.5 ø,0.0ø,0.5ø, 1.0ø, and 1.5øC). he numberof pointswithin eachof thesewindows
are 4, 19, 25, 21, 11, 9, and 11, respectively.
Severalstudies ttempted o explain he Hurst phenomenon
basedon statistical rguments nd models.Brasand Rodriguez-
Iturbe [1985] summarize he different ines of thought n ex-
plaining the Hurst phenomenon s due to (1) a transitory
behavior due to the short records of observedgeophysical
variables seeSalas t al., 1979,Figure5], (2) nonstationarityf
the underlyingmean of the process seeKlemes,1974;Potter,
1976;Beesand Salas,1978;Bhattacharyat al., 1983],and (3)
a stationaryprocesswith very large memory.
A physically asedexplanationor the Hurst phenomenonn
the Nile flow s hypothesized.he aboveanalysisndicates hat
the occurrence of ENSO events excites similar oscillations in
the tropicalclimate,which are then teleconnectedo the Nile
flow through he rainfall-producing echanismst the sources
of the Nile. The relation of the ENSO index and the Nile flood
suggestshat the Nile flood responds o natural variability n
SST of the Pacific Ocean. This variability occursat several
timescalesanging rom annual o decadaland even onger.As
a result,variability n SST of the PacificOceancauses ignifi-
cant nonstationarityn the mean of the annual low processn
the Nile River. Natural climatic actors other than ENSO)
dictate he variabilityof the Nile flow around he varyingmean
of the process.
The relation between ENSO index and the nonstationary
mean of the annual flow in the Nile is estimated. This relation
is shown n Figure 5. The annual low of the Nile is averaged
over a small window of ENSO indices, each with a width of
0.5øCcentered around -1.5 ø, -1.0 ø, -0.5 ø, 0.0ø, 0.5ø, 1.0ø, and
1.5øC. he numberof pointswithin eachof thesewindows re
4, 19, 25, 21, 11, 9, and 11, respectively. ach group of points
is treated as a sample rom a differentpopulation.Although
someof thesesamples ave only few data points, he nonsta-
tionary mean of the Nile flood is clearly related to ENSO
index.The resulting elation s described y
mean of the annual flow of the Nile
= 88.5 - 8.7 (ENSO index) (1)
The coefficient of correlation in this relation is -0.9. The
varyingmean of the annual low n the Nile River is computed
in Figure6 using 1) and the seriesof observed NSO indices.
Figure 6 shows he varying mean for the years 1872-1972.
These random oscillations epresent he contributionof the
ENSO index to the natural variability n the flow of the Nile
River.
Basedon this analysis, e propose he followinghypothesis:
the mean of the annual low processn the Nile River varies n
time followingENSO, resulting n a non-stationary rocess,
and causing he Hurst phenomenon. he statistical haracter-
isticsof nonstationary rocessesavebeen studiedextensively,
and their ability o reproduce he Hurst phenomenon asbeen
proven [see Potter, 1976; Bees and Salas, 1978]. In order to
excludeeffectsdue to the transitorybehaviorof the process,
the hypothesis resented n this paper can only be rigorously
tested hen ong imeseries---103 atapoints) f theannual
flow in the Nile River becomes available.
Our hypothesis bout the Hurst phenomenon s similar to
the argumentofferedby Potter 1976]. He analyzedprecipita-
tion records rom North America and pointed o the potential
role of oscillationsn the stateof the globalocean-atmosphere-
land system n providinga physical xplanation or the Hurst
phenomenon.However, his analysis as ocusedon a specific
global oscillation, he ENSO, and the hypothesis resented s
relevant to a different natural variable, the Nile flood.
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136 ELTAHIR: NATURAL VARIABILITY IN FLOW OF THE NILE RIVER
lOO
85
80 i i i i i i i i i i
1870 189o 191o 1930 1950 1970
y•ar$
Figure 6. The varyingmean of the annual low process sti-
mated rom observed NSO indices nd using 1).
In summary,he hypothesis escribedn this section s mo-
tivatedby the following.
1. The analysis resented n this paper confirms he exis-
tence of a significant elation between he mean of the Nile
flood and SST of the PacificOcean seeFigure5).
2. The SST of the Pacific Ocean exhibits oscillations at
several imescales, anging rom annual to decadaland even
longer seeWangand Ropelewski,995,Figure5]. Hence the
mean of the Nile flood processoscillatesn time too (see
Figure6). As a result,SST of the PacificOcean ENSO index)
and the Nile flood representa weaklycoupledbivariatenon-
stationarystochastic rocess.
3. Several of the studies listed above have shown that non-
stationarystochastic rocesses re capableof simulating he
Hurst phenomenon.
The combination f these hree factorssuggestshat offering
the connection between SST of the Pacific Ocean and the Nile
flood as a potentialcandidate or explaining he Hurst phe-
nomenon s a reasonable ypothesis.
Conclusions
The analysis f the Nile flow and ENSO indexsuggestshat
natural variability n the annual low of the Nile River can be
decomposednto two components: mean that varies n time
followingENSO, and a random luctuationhat occurs round
the varyingmean due to climatic factorsother than ENSO.
The nonstationarymean and the random fluctuationexplain
25% and 75% of the observed atural variability, espectively.
The relation betweenENSO and the Nile flood has mpor-
tant implications n two importantproblems: redictability f
the Nile flood, and explanation f observed tatistical harac-
teristics f the Nile floodseries the Hurstphenomenon).he
fact that ENSO events an be predictedwith reasonable ccu-
racyat a lead time of about 1 year suggestshat the correlation
betweenENSO and the Nile flood shouldbe used o improve
the predictabilityof the annual flow in the Nile River. The
finding hat the Nile flood seriescan be decomposednto a
varyingnonstationarymean and a random fluctuation avors
the line of thought that the Hurst phenomenonmay be due
to nonstationarity n the mean of the process.For this rea-
son, we present the hypothesis hat ENSO is the causal
factor for the Hurst phenomenon n the annual flow of the
Nile River.
A simpleprocedure or predictionof the Nile flood is pro-
posedand illustratedby application or the years1973-1989.
The conditional robabilities f havinga low, average, r high
flood n the Nile River are computedgiven he SST conditions
in the PacificOcean.The new procedure s designedo utilize
model predictions f SST n the PacificOcean. n the absence
of thisprocedure,he bestpracticalprediction f the Nile flood
would e hemeanlow -•90 km3). heanalysisresentedn
this paper suggestshat the proposed roceduremproves n
thisprediction.Suchan improvementn the Nile flood predic-
tion shouldhavea positive mpacton water resources anage-
ment in Egypt, particularly n operationof the High Aswan
Dam.
Future researchwill focus on further developmentof the
floodpredictionprocedure. he emphasis ill be in combining
SST measurementsnd predictionswith other inputs,suchas
hydrologicalmeasurementsf rainfall and streamflowo im-
prove he predictionof the Nile flood.
Acknowledgment. The author is grateful to StephenE. Zebiak of
Lamont-Doherty Geological Observatory,Columbia University, or
providing he predictions f SST n the PacificOcean hat are used n
this study.
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