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



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.



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


Figure 4. Categories f the Nile flood and ENSO index.The numberof data points n eachgroup s also

shown.




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.



ELTAHIR: NATURAL VARIABILITY IN FLOW OF THE NILE RIVER 135

lOO

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2


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.




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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el nifio and the natural variability in the flow of the nile river

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