e hydrology er

P - *D

I

42 J.M. d'Herbès, C. ValentinlJourna1 of Hydrology 188-189 (1997) 18-42

Poesen, J., 1986. Surface sealing on loose sediments: the role of texture, slope and position of stones in the top layer. In: E Callebaut, D. Gabriels and M. De Boodt (Editors), Assessment of Soil Surface Sealing and Crusting. Flanders Centre for Soil Erosion and Soil Conservation, pp. 354-362.

Rahman, H., and Dedieu, G., 1994. SMAC: a simplified method for the atmospheric correction of satellite measurements in the solar spectrum. Int. J. Remote Sensing, 15(1): 123-143.

Rajot, J.L. and Esttves, M., 1994. Cartographie des états de surface de petits bassins versants de la région de Niamey. ORSTOM, Niamey, IO pp.

Roose, E., 1981. Dynamique Actuelle de Sols Ferrallitiques et Ferrugineux Tropicaux d'Afrique Occidentale. Etude Expérimentale des Transferts Hydrologiques et Biologiques de Matiitres sous Végétations Naturelles ou Cultivees. ORSTOM, Paris, Collection Travaux et Documents, No. 130, 569 pp.

Roose, E. and Piot, J., 1984. Runoff, Erosion and Soil Fertility Restoration on the Mossi Plateau (Central Upper Volta). International Association for Hydrological Sciences, Publ. No. 144, pp. 485-498.

Seghieri, J.. Galle, S. and Rajot, J.L, 1994. La brousse tigrée dans le Sahel nigérien: étude de la cofluctuation du stock hydrique et de la végétation annuelle. In: 20th Hydrological Meeting, ORSTOM, Montpellier, pp. 603- 613.

Soil Survey Staff, 1975. Soil Taxonomy. A Basic System on Soil Classification for Making and Interpreting Soil Surveys. Soil Conservation Service, US Department of Agriculture, Agriculture Handbook No. 436, Washington, DC, USA, 754 pp.

Thiéry, J., d'Herhès, J.M. and Valentin, C., 1995. A model for simulating the genesis of banding patterns in Niger.

Valentin, C., 1986. Surface crusting of arid sandy soils. In: F. Callebaut, D. Gabriels and M. De Boodt (Editors). Assessment of Soil Surface Sealing and Crusting. Flanders Research Center for Soil Erosion and Soil Con- servation, Ghent, pp. 40-47.

Valentin, C. and Bresson, L.M.. 1992. Morphology, genesis and classification of soil crusts in loamy and sandy soils. Geoderma, 55: 225-245.

Valentin, C, and Casenave, A., 1992. InfiIrration into sealed soils as influenced by gravel cover. Soil Sci. Soc. Am. J., 56: 1167-1673.

Van der Watt. H.V.H. and Valentin. C., 1992. Soil crusting: the African view. In: M.E. Sumner and B.A. Stewart (Editors), Soil Crusting. Chemical and Physical Processes, Advances in Soil Science. Lewis Puhl., Bocd Rnton. USA, pp. 303338.

Vandervaere, J.P., Jaramillo, R.A., Peugeot, C. and Vauclin, M., 1994. C;tractCrisation hydrodynamique in situ de sols encroiltés. In: 20th Hydrological Meeting, ORSTOM, Montpellier, pp. 603-6 13.

West, L.T., Wilding. L.P., Landeck, J.K. and Calhoun. F.G., l9S4. Soil Sorvey of the ICRISAT Sahelisn Center, Niger, West Africa. Texas ALM University System, College st:ition, Texas.

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J. ECO^., 83: 497-507.

, .'

Journal of Hydrology

E L S E V I E R Joumal of Hydrology 188- IS9 ( 1997) 43-73

Rainfall climatology of the HAPEX-Sahel region during the years 1950- 1990

L. Le Barbé', T. Lebelbs* "ORSTOIWLTHE Groupe PMO. BP 5'045. 34032 Montpellier Cr&r 1. Frclnce

hORSTO~WLTHE. Groupe PRAO. LTHE-CNRS, ß P S3- 38041 Gretroble Ce1le.r 9, France

Abstract

In the Sahel. rainfall is the single most important factor conditioning the hydrology and ihr. climate. but comprehensive statistical analyses o f the rainfall climatology in the region are rare. Yet. even though in the Sahel rainfall data are scarce by the standards of the temperate countries, it i5

shown here that it is possible to obtain a reasonably good idea of what the rainfall has been over Sahelinn Niger for thc past 40 years. both in ternis o f interiinnual variability ;und spatial distribution. T o that nim a st:itistical model is used, which deconiposes the space-tinir fluctuations of long-term rainfall averages into the fluctuations of the nieiin event rainfall on the one hand, and of the mean number of rainfall events over any period of accumulation. on the other hand. This model is first

sis of monthly rainfdl data over the whole of Niger. I t is shown that the lasting ntcted Niger for niore than 20 years is associated with a decrease in the number

of rainy events. rather than to a decrease of the mean event rainfall, and that this decrease is more pronounced for the core of the rainy season. Because these fluctuations are not homogeneous over Niger. :i 5" x 4' zone centred on the HAPEX-Sahel 1' x I " square is selected in order to characterise more nccurately the ruinfall climatology o f the HAPEX-Sahel area hetween 1950 and 1990. In comparison with what i t w3s b c t w e n 1950 and 1970, the averiige length of the rainy season has not changed significantly during the dry period 1970-1990. Rather. i t is the decrease of rainfall in July and August t h a t explains most o f the diminution o f the totiil annuiil riiiiifiill over this part of the Sahel since 1970. The average number of rainy events in August was reduccd by about 30%. while thc mean even1 rainfall remnined roughly constant. Fin:illy, the analysis of thc daily rainfall series for Ninmey (which constitutes the longest record available in Niger. skirting in 1905) enables the comparison of four periods of 20 years between 1910 and 1990. The period 1970-1989 appears to be by far the longest and most severe dry spell of the past century. Almost 90% of the annual rainfall decrease over this period is explained by the decrease of the nic:in numher of rainfall events during July and August, while both the length of the rainy season and the mean event rainfall remained slable.

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44 L. Le Barbé, T. LebelIJoirrnal of Hydrology 185-189 (1997) 43-73

1. Introduction

There is a striking mismatch between the estreme vulnerability of life in the Sahel to frequent rainfall deficits, and our limited knowledge regarding the rainfall climatology of the area. Speculations on the links between the drought and changes in the atmospheric circulation have been numerous since the early work of Bryson (1973). It has often been supposed that dry years over West Africa are caused by a southward displacement of the average intertropical convergence zone (ITCZ) position (e.g. Winstanley, 1973; Kraus, 1977). This should go with a reduction in the length of the rainy season, a fact opposed by Nicholson (19S1). To paraphrase Gregory (19S2) it could he stated that, during the SOS, opinion about the nature and the statistical significance of the Sahelian drought has fluctuated almost as much as the rainfall conditions themselves. As underlined by Janicot and Fontaine (1993), this may be partly attributed to the variety of mechanisms involved. Recent progress in an approach pioneered by Lamb (197Sa.b) has emphasised the link between the sea surface temperature (SST) anomalies at a global scale and the interannual variability of the Sahelian rainfall (Folland et al., 19S6). Since, these anomalies are themselves the result of complex interactions between various atmospheric and continental processes which are not yet fully understood, there is ample room for additional studies aiming at a better characterisation of the interannunl v;iri;ibility of the Sahelian rainfall.

Today, evidence has been gained that the drought of the 70s and early 80s was not bound to end rapidly. In Niger, as shown below for the period 1970-1959 (and in Lebel et al., 199.5, for the years 1990-1993) the drought has lasted continuously for 25 years (1 969-1993) Thus, it is now possible to carry out meaningful statistical studies to characterise the space-time rainfall distribution during this dry spell ils compnred with that of the previous wetter period. This paper is devoted precisely to such ;i study. I t limits itself to the HAPEX-Sahel (H-S) region (see Goutorbe et al., 199.4, for ;i description of the HAPEX-Sahel location and setup) and is based on a statistical model tuned to the characterisation of the space-time fluctuations of long-term rainfall averages. The model dlows for a distinction to be made between vnriations in the number of storms and variations in the mean storni rainfall. While our results ilre valid for the Central Sahel only, it is believed that the model could be applied fruitfully to thc whclle of the Sahel, '

provided Lhe tinta nectlcd ;ire collectctl. Morcover, ;IS recognisctl by Jmlicot iind Fontaine ' (1993), there does exist an overall zonal homogcneity of the Sahclian rainkill climatology. It is consequently reasonable to suppose that the major conclusions ol' this s!udy ;ipply to most of the Sahel.

A preliminary analysis of the monthly rainfall dnto f o r the whole o f Niger shows . that the recent dry period is chnracterisctl by ;I clccrensc in thc nuniber of rainy ' events, while the mean storm rainfall varies little. This first result has encouraged us to proceed further by applying our model to the nnalysis of a larger data set covering a 5" x 4" zone centred on the H-S I " x I " sclitxrc :tnd to thc comparison

' of the rainfall time distribution in Niamey for periods of 20 years between 1910 and 1990. The results obtained over the whole of Niger were confirmed, which led us to undertake a detailed investigation of the rainfall fluctutitions as a function of the latitude and the period of the year.

I i I 1

i ! I I

i

l

! i I

3

1 I

l

I

i I i

1 i j I

I

I

45 L. Le Barbé, T. LebellJoiimal of Hydrology 188-189 (1997) 43-73

2. The data

The longest daily rainfall series available in Niger are those from Niamey and Zinder, which both started in 190.5. Other stations began to operate in the following 20 years but it was not until after the secondworld war that the raingauge network became dense enough to provide a reasonably good coverage of rainfall for climatological studies (see the reports

Table 1 Names and coordinates of the 35 raingauge network used to analyse thc rainfall climatology of Niger between 1950 and 1989. The relativc annual rainfall decrease between the period 1950-1969 (JI) and the period 1970- 1989 (E) is given in the lilst column

Station Longitude Latitude Annual cv [R(Jl) - R(J2)]! 50-89 R(J1) R 50-89

Ag;idez Ayoroii ßi lma Birni n gioiirc Dirn¡ n koririi Bouz:~ D i f h Dogondoutclri Dosso Filingue Gay:1 Golllcyc Goudoum:iri;l Goure Guitlinlollni 1llcl;l kl0

K o l o b1;ld:l~llI~l

M:ig:iri:i Mninc sortxi M m d i Myrrinh N giiignii Ni:imcy airport Ni:inicy ville ou;lll;lnl

-f;lllou:l I';lnoul Ter;!

Ti I I:I hery Toukounous Ziiidcr

say

~ r c s ~ : l ~ l a ~ l

7.98 0.85

12.92 2.90 5.2s 6.05

12.62 4.00 3.18 3.30 3.45 I .SS

11.17 10.30 055 5.25 57.5 2.35 5.0s S.lJ.1

I 1.0s 7.11s (J.15

13.12 2.15 2.13 2.05 2.35 5.25 H.82 0.82 7.0s I .45 8.50 8.08

16.97 14.75 18.68 13.0s 13.80 14.42 13.42 13.63 13.02 14.3s I 1.8s 13.82 13.72 13.0s 13.6s 14.47 15.23 13.30 14.12 I2,'IS 13.23 13.47 13.72 14.2.5 13.4s 13.50 14.32 I 3. I o I4.YO 14.05 14.03 13.75 14.20 14.5s 13.78

138 0.469 313 0.264

14 0.853 568 0,218 534 0.278 43 I 0.260 288 0.367 52 I 0.3.58 607 0.206 43s 0.350 I: I o 0.ISI 4.52 0.2114 31.5 %330 335 0.38 I 36.5 0.30h 423 0.26s 202 0.336 SOO O.2AS 43(1 0.33 I Sh4 0.1.17 3'17 0.202 54 I 0.373 J.ì0 0.3S(I 21s 0.48s 5hh 0313 564 0.21s 434 0.321 613 0.2311 350 0.262 270 0.423 537 0.2hO 4.56 0.2S-l 445 0.300 330 0.357 460 0.263

0.463 0.286 0.486 0.251 0.265 0.229 0.310 0.355 0.211 0.404 0.072 0.250 0.269 0.4 17 0.2 13 O. 179 0.139 0. 105 0.322 0.205 0.2 I4 (1.3 13 0.366 0.360 0.241 o. 19.5 0.403 0.208 0.286 0.4 I2 0.284 0.33 I 0.339 0.371 0.275

. .

! . .

46 L. Le Barbé, T. LebellJournal of Hydrology 186-189 (199? 43-73

from CIENORSTOM, 1986, and CIEH/ORSTOM, 1990, for a detailed account of the evolution of the Niger raingauge network).

Niger is a country extending from 12"N to 24"N, well into the Sahara desert. Never- theless most of the population live in the south where regular agriculture is possible. Even though there are no absolute and undisputed latitude limits for the Sahel, Niger may thus be divided into two regions of roughly the same area: one, essentially desert, north of the 17" parallel, and one, Sahelian, south of this limit. Naturally the pattern of the raingauge network reflects the concentration of human activities in the south. Among 35 daily rainfall stations which operated continuously, with no more than 10% of missing data at any given station, between 1950 and 1990, 34 are located south of the 17" parallel and 33 south of the 15" parallel (Table 1 and Fig. 5 to be discussed later). Two different analyses will consequently be carried out. The first concerns the whole of Niger, and is based on the network listed in Table 1. The second analysis aims at providing a meaningful climatology for HAPEX-Sahel. It is thus restricted to a 5" x 4" zone (0"-5" in longitude, 11"-15" in latitude) centred on the H-S 1" x 1" square, hereafter referred to as the CSA (Central Sahel area). In order to minimise the border effects and to work on a larger sample of stations, all the raingauges available on a region extending 2" westward and 1" eastward of the CSA (Fig. 1) have been used for this analysis. Nineteen synoptic and climatic stations operated from 1950 to 1990 over this zone that covers south-east Burkina, south-west Niger and northern Benin. As well as these 19 stations, 57 additional raingauges have been used for the period 1950-1989, and a further 39 for the period 1970- 1989. Fig. 1 shows that the enrichment of the network for the period 1970-1989 is *,

47 L. L E Barbé, T. LebelfJournal of Hydrology 186-169 (1997) 43-73

,

I

I -1 O 1 2 3 4 5 6 II

-2

Longilude : &jmopfic or climofologic sfafiom : Addifiomb sfofions 1950- 1970

O: Addirionab sfafiom 1970- 1990

Fig. 1. The raingauge network over eaqtern Burkina and western Niger. Climatological and synoptic stations are indicated with their names. Other stations are indicated only by :I symbol (O. slations started before 1970; O, stations started after 1970). The Central Sahel area (CSA), defined for studying the modification of the rainfall space-time distribution after the onset of the drought, is delimited by the vertical full lines, while the HAPEX- Sahel study area is the central square. delimited by dashes.

I

especially important over the Niger part of the CSA. Working on a strip extending beyond the borders of Niger, into Burkina, allows us to obtain a sufficiently large sample for the computation of averages along latitudes for the period 1950-1969.

3. The leak distribution as a model of the rainfall regimes in tropical Africa

3. I. General presentation of the nroclel

The regional analysis of rainfall regimes requires modelling which is coherent both in space and time. This goal is best achieved when the parameters of the model have a physical content. For any given period of rainfall accumulation, the mapping of these parameters then leads to a meaningful characterisation of how the rainfall varies in space. Also, the evolution of these parameters with the time of rainfall accumulation bears a direct climatic signification.

The model proposed here to describe and analyse the rainfall regime of Sahelian Niger, known as the leak distribution, is rooted in the renewal theory (e.g. Cox, 1964). To our knowledge it first appeared in the literature as a special case of the compound Poisson processes, proposed by Einstein (1937). I t was then applied to rainfall analysis by Ribstein (1983), Le Barbé and Lebel (1589) and Le Barbe et al. (19S9). The short presentation given below is taken Lion1 Le Barbé ant1 Lebel (1989).

Let R be the slorni point rainfall accumulation. R is supposcd to be exponentially distributed, conditionally on the rainfall being non-zero (all the statistical analysis in the following applies to non-zero rainfall). Such an assumption was applied to storm rainfalls in southcrn United States by Smith and Schreiber (1974), followed by severnl

Niamey ABroport 1946-1 981

I I I I 1.

Event rainfall (mm) Fig. 1. Distrihiilion of the event r:k¡nfitll for Nimley (I 946- 19SI).

,'; . J I

48 L Le Barbé, T. LebeWJownal of Hydrology IS8-lS9 (1997) 43-73 I

other authors. The climate of Arizona has some common features with that of Niger. It is semi-arid and storms are easily separable. It was therefore expected that the assumption of an exponential distribution of the event rainfall should hold for Niger as well. Fig. 2, where an exponential distribution is fitted to a series of 515 event totals recorded in Niamey by a tipping bucket raingauge between 1946 and 1981 (there are numerous missing data in this series, which explains why only 515 events are available over 36 years, see Bouvier, 1986, ' for details) clearly supports this hypothesis.

The c.d.f. (cumulative distribution function) of R may thus be written: 1

~ ( r ) = I (1)

and the p.d.f. (probability density function) is:

1 -r/s f (r)= -e S

where s is the mean and the standard deviation of the storm rainfall. For climatically' homogeneous periods, s is assumed constant.

The number of storms, N, over any period T i s further assumed to be a Poisson distributed random variable, that is:

e-'T.iy P ( N ) = - N !

(3)

where i r i s the mean number of storms over period T. For a given number of storms, I I , the rainfall accumulation over period T, denoted RT. is then Pearson III distributed, (see e.g.. Brunet Moret, 1969, for a comprehensive study of this distribution) with p.d.f.:

e - ~ r / ~ R ( ~ ~ - ~ ) ' T f (RT/N=n;n>O)=

f ( J ? - I)!

Defining U,, as the scaled variable Rds, it becomes:

The marginal distribution of Ur, letting II vary from I to infinity is then:

or:

* (AT.U,Y ,,=o (n!).(n f l)! Let J = C

then J may be written:

J = I I ( 2 G ) I ( G )

(4)

(7) .;

49 L. Le Barbé, T. LebbellJournal of Hydrology 188-189 (1997) 43-73

where Ii(2-) is the modified first order Bessel function. The distribution of RT is thus given by:

with UT = R ~ l s , and:

F(O) = e-'T

The first three centred moments of the leak distribution are:

which allows computation of the coefficient of variation and the skewness coefficient:

( 1 3

(16)

cv = [3/X,J"2

y1 =3/[7x.1.]"2

Since the two parmeters of the leak distribution are the mean event rain depth and the mean number of rainy events over the period Tconsidered, their mapping permits a study of how the variation in the :iver:ge rainfall is related to the fluctuations of these two factors. In this respect our model i s conipariible to the one used by Garbutt et al. (19SI). However, and tis fxr as the hypothesis of the time stationnrity of the mean evelit rxin depth s Iiolds, i t has the ;idilition;il adv;int:igc of niaking possiblc the deduction of the distrihutiori of rainf;\ll over any period T' = k.T from the distribution computed for the period T (s'=s and A' , = k.XI) .

'rhc leak dislribution (t1icre;iftcr tlcnotcd LD) ciin lie fitted to il scries of rainfall cuiI1u- Iatctl over any given period T, providcd that: ( i ) 7' is long :IS coniparcd with the me;~n duration (il' ii rainy event: (i¡) the rninfiill process is tinic-stationnry over T (thiit is s is constiint). This I:iticr :issumption niay Iw sonicwliat rc1;tsecl ~ i i d e r ccrt;iin conditions, hut we will not mukc use o l this possibility hcrc. The LD fitling is bascd on the inference of Iwo piiriiiiiclcrs, LDI and LD7, that arc uscd ils estinxltcs of s arid Ar, respectively. Although this infcrcncc. using cl;issic;d iippronclics such :IS lhe niomcnt o r maxilntlnl likclillood (ML) nictliotls is relatively easy to carry out coniputationally speaking (see Babusinus, 1969, and Ribstein, 1953, for the formulation of thcse algorithms), i t niay involve some distortion in the description of the underlying rniiihill process. The m;ijor c;iuse for such distortions is the correlation existing between the two estimates for both methods cited above (Bnbusiaux, 1969):

50 L. Le Barbé, T. LebeIlJournal of HydroIogy 188-189.(1997) 43-73

The correlation coefficient between LD1T and LD2T depends on AT only, and it tends towards 1 for large values of AT, while it tends towards O for small values of AT. Thus, AT should be kept as small as possible, by choosing short periods for T. In practice two durations are most often used in rainfall climatology studies, that is 10 days and 1 month, for reasons linked either to modelling purposes or convenience (data availability). For a monthly mean number of events of 9 (an average value for September in the Sahel), the r square is equal to 0.90 when working on monthly totals and 0.77 when working on 10-day totals. For a monthly mean number of events of 6 (an average value for June in the Sahel), the r square is equal to 0.96 when working on monthly totals and 0.47 when working on 10-day totals (a comprehensive study of the correlation effect and associated estimation error variances of LDIT and LDZTwill appear in a forthcoming paper). Since the underlying hypothesis in the building of the LD is that s and AT are independent this correlation is embarrassing. In particular, when comparing hvo stations or two different periods of observation at the same station in order to detect possible modifications in the rainfall climatology, the interpretation of changes in the value of s and AT will be made more difficult due to possible compensation effects in the estimation procedure (thus exaggerating or attenuating the real increase, or decrease, of one parameter).

Therefore an alternative method is proposed utilising the average number of dry days do over a period T of d days, which is information that is not used i n the moment and ML methods. Eq. (11) gives direct access to an estiniatc of Xr as:

LD2r = -LN (s) where N o is the number of observed dry sequcnces of length Tand N is the total observed number of sequences of length Tin tlie sample. The computation of LDI is then based on a no-bias condition:

LDlT = - A T (19) * A

LD2 where

The ratio No/N is an estimate of the probability, denoted FU, of zero rainfall over the period T. The obvious advantage of this FO algorithm is that LDZ7 is estimated independently of LDlrand that it makes use of important information on the Poisson process. The conipensation effects mentioned above for the momcnt and ML methods :ire thus reduced, as demonstrated by comparing the correlation coefficient of the cstimatcs, given by thc following formula:

is the sample mean,. used as an estimate of E[R7]

r(LDIT, LD2T) = (- 1 + A) with the correlation of the ML and moment estimates given in Eq. (17).

For small values of AT the correlation cocflicicnt tends towards zero. I t also tends towards 1 when AT tcnds towards infinity. There is thus a major advantage to working on samples characterised by a low value of hr. Selecting T = I day is an cfficient way in that direction. In the Sahel A7(T = 1 day) will remain below 0.6 and the correlation coefficient between the estimates of the daily LDI I (denoted LDL) and LD2¡ (denoted

51 L. Le Barbé, T. LebelIforunal of Hydrology 188-189 (1997) 43-73

LD2) will be kept below 0.3 in absolute value (r(LD1, LD2) = - 0.27 for A, = 0.6 and r(LD1, LD2) = - 0.14 for XI = 0.3). Consequently the following procedure for estimating L D l r and LDZT has been followed here:

1. estimation of the daily values of LDl(i) and LD2(i) for each day i of the period T of interest, estimating FO as:

FO = duld

where do is the average number of dry days during period T of d days; 2. estimation of LDIT and LDzT as:

I d LDlT= - dir1 2 LDl(i), and

rl LD2,= ,I1 LDZ(i)

1 - ( 2 3 )

In Section 4 below tlie period Tconsidered is 1 month ( d = 30 or d = 31). When working on a sample of 20 years, FO is thus determined from a total number of 6000 daily observations. In Sections 5 and 6, a moving window of 11 days is considered and there arc stili 2200 observzitions to estimate FO from a sample of 20 years. Consequently, the two main advantagcs of the method are (i) ensuring a low corrclation between the parameter estimates and (¡¡) ;illowing i~ robust cstim;ition of FO :ind thus of LDZT. Its we:iknchh lies in using daily rainkill data For the dctcrniination ol' the number of dry days, sincc ;I rainfiill event may be spread over two different days, even il' lasting for a few hours only. Nonetheless the probability of such an occurrence is rcduccd by the fact tha t daily readings ;ire inatlc at S:OO am., a n hour of lowcst ra in f i i l l probability due to the diurnal cycle ol' convcclion. Furthcrmorc ;I study ciirricd o u t o n flic EPSAT-Niger data has shown that tlic avcrogc duration of ii convcctivc storni in the Sahel is around 5 li (Lebel et :il., 1007. this

I t slioulrl l x noted that. since the sum ol' II Poisson distribtitions is sti l l a I'oissoli tlislribution the LD model is valid for all dur;itions bctwccn I day and 1 month. Howcvcr, since the LDZ ( = 1) csfini;ltc is not ;I 1iiic;ir firriclion of the tl;~ta, the LD23,) estiniatc is gcncrnlly not identicol whether computcd directly from monthly rainfall datu or ÍIS the suni of the 30 (or 3 I ) daily LD7 cstiniatcs. l'liis is tlie price to pay for obtnining an cffectivc pmmctcr directly I'rom monthly data which iirc casier to acccss and to process. Conipar- ¡sons m:itlc Ihr a few stations belonging to both the snmplcs uscd in Scctions 4 and 5 \lave shown that tlil'fercnccs do not cxcccd 10%. x i accuracy which is sufficient for a glo1i;il andysis o f monthly rainfall regimes, as carricd out in Section 4.

issue).

4. 1i:iinfall oyer Niger for the period 1950-19S9

- As for thc whole of continental West Africa. the roinfiill rcgirlic of Niger is under the depcndcncc of the north-south migration of the ITCZ. North of tlie ITCZ, high pressures originating from the Sahara prcvcnt any rainfall. exccpt in the case of rare descents of cold

. ..

52 L. Le narbt?, T. LcbcllJourrral of Hydrology 188-189 (1997) 43-73

air from the north during the boreal winter. Rain thus occurs over a given area only after the ITCZ has moved past this area towards the north. The maximum northward extent of the ITCZ is reached in August, corresponding to the period of maximum rainfall over the. Sahel. The movement of the ITCZ northern edge is not regular which is the cause of often’ erratic starts of the rainy season. Even when the rainy season is well established sudden retreats southward of the ITCZ are not uncommon. The annual rainfall depends heavily on the duration of the rainy season, that is on the mean time during which the ITCZ is positioned north of the point considered. As a consequence, the yearly average isohyets are oriented east-west (Fig, 3), with a north-south gradient-of roughly 1 mm km-’ (the average yearly rainfall varies from 140 mm in Agadez to 720 mm in Gaya, separated by 560 km in latitude). Note, however, that in the eastern part of the country (region of Zinder and Lake Chad) the isohyets dive south-eastward.

The 40 years average over the H-S study area ranges from about 600 mm in the south (13”N) to a littleless than 500 mm in the north (14”N). The average of Niamey over this period (564 mm) is close to the areal average which can be computed by integrating the isohyetal map of Fig. 3 over the H-S square (560 mm).

AVERAGE ANNUAL RAINFALL (mm) 1960 - 1989 . - ..-. -.. a--

----_. ..--.-_ /--- -- ‘./* i

:, ‘. !.,

i ,/-

,,a’

,I

13

O 2 4 ¿ i IO 12 14

Longitude

53 L. Le Barbé, T. LebellJoiiriial of Hjdrology 188-189 (1997) 4-7-73

4.1. The Joseph effect nffectirig the mirfnlI irr Niger

The last 40 years have witnessed a modern remake of the 7 dry-7 wet years sequence that introduced Joseph as the first climatologist of Africa during the pharaonic era. In their paper “Noah, Joseph and operational hydrology”, Mandelbrot and Wallis (1968) have coined the expression “Joseph effect” to “designate the fact that a long period of high or low precipitation can be extremely long indeed”. The lasting drought which has plagued West Africa since the end of the 60s was documented early in the SOS (Nicholson, 1950, 1981; Lamb, 1982,1953). This drought continued throughout the 80s and it constitutes the most recent example of this Joseph effect, which Mandelbrot and Wallis believed was an intrinsic characteristic of rainfall regimes, rather than an unexpected accident. This drought has been especially severe over Niger, as may be seen from Fig. 4, where the fluctuations of the following scaled rainfall index I,(k) are shown:

where X ( i , k) is the annual rainfall at station i for year k, and n(i) is the annual average over the reference period for station i. I is the total number of stations used for the computation

Deviation from the scaled centred rainfall (Niger)

2 1

-2 ’ I

5 0 5 5 6 0 6 5 7 0 7 5 8 0 8 5 9 0

Years

Fi&!. 4. C’iiri;ition of Ihc rainlhll indes for Nigcr hclwci, I W l :i1111 1990.

. . f i c.:,. .’

I

54 L. Le Barbé, T. LebellJournal of Hydrology 188-189 (1997) 43-73

(a subset of 20 stations homogeneously spread over the territory was chosen, out of the 35 stations of Table 1, to build the graph of Fig. 4). As previously noted by Hubert and Carbonnel (1987) and Hubert et al. (1989) the

persistence within each period is striking: all years before 1968 have a positive rainfall index, while all years, but one, after 1968 have a negative rainfall index. Fig. 5 shows that this general decline of the rainfall over Niger is equivalent to a 150-km southward shift of the annual isohyets during the dry 1968-1989 period. However this general trend masks important differences from one station to another. Excluding the two northern-most stations (Bilma and Agadez, north of 16"N) the relative rainfall decrease between the period 1950-1967 and the period 196S-19S9 varies from 7% (Gaya) to 43% (Goure, Tanout) (Table 1). The maximum absolute decrease reaches 220 mm'in Filingue (from 545 mm to 325 mm) but it was only 60 mm in Gaya (from S53 mm to 792 mm).

A better understanding of this phenomenon can be obtained only by analysing how it has affected the rainfall distribution within the rainy season: has the contribution of each month remained stable or has it changed? Secondly, was the proportion of strong versus

Annual isohyets (m) forthephds 1950-69 (dashed lines) andi970-89 (full lines) O 2 4 6 0 10 12 14

I ' ' I ' ' i ' I ' \ I ' I ' I 24- -24

22- -22

20- -20

3:'

Lcmgituck

Fig. 5. Comparison of the annual isohyets between the period 1950-1969 and f l i t period 1970-1939. On average there is a 100-mm soufhward shift during the lY70-1YS9 dry period.

55 L. Le Barbé, T. LebeltJotirnal of Hydrology 158-189 (1997) 43-73

56 L. Le Barbe, T. LebellJoicrnal of HydroIogy 188-189 (1997) 43-73

medium or weak rainfall events modified? We seek to answer these questions by examin- ing the evolution of the parameters of the leak distribution fitted to monthly totals, that is we assume in a first step that the rainfall process is time stationary over a period of 1 month. Although calendar months are not necessarily meaningful from a climatic point of view, they constitute the most convenient entities to reach a synthetic characterisation of the changes into the intra-seasonal rainfall distribution. An alternative to the monthly average approach will be proposed in Section 5 to analyse with more detail the space- time fluctuations of rainfall over Central Sahel.

4.2. Modijcatioii of the nzoiitlz[y raitlfnll diiring the recent dry period

The drought in Niger started in 1968, as can be seen from Fig. 4. Lebel et al. (1995, 1997) have shown that it lasted until 1993. A break was observed in 1994. In other parts of the Sahel, especially those forming the western part of the Central Sahel area (CSA) studied below, the start of the drought was delayed by 1 year or 2. By the beginning of the 70s though, the drought was well established everywhere, as shown by Gregory (19S2). In order to deal with periods of equal duration when comparing the wet and dry spells that occur in succession, we will thus consider in the following a wet period (Jl) of 20 years between 1950 and 1969, and a dry period (52) of 20 years between 1970 and 1989 (as seen in Fig. 4, the years 1968 and 1969 were moderately dry in Niger anyway). Ending the period of analysis in 1989 will provide an independent reference to be used by Lebel et al. (1997) for the analysis of the rainfall climatology during I-IAPEX-Sahel (1990-1993).

Ayorou - June 1970-1989

Pearson 111 Leak Distribution

- ....... - ....

t

O 1 2 3 4 5 6

- (LOS(1 -F ) )

Fig. 6. Leak, Pcarson 111 and Gaussian distribulions fitted lo the June monthly r;iiiifall series of Ayorou (1970- 1989).

L. Le Bari)é9 T. LebellJonrnaI of Hydrologv 188-IS9 (1997) 43-73 57

The leak distribution has been fitted month by month for the 35 stations of Table 1, separately for the two periods J1 and 53, using the FO algorithm. Six months, May through October, were selected, which account for 99% of the annual rainfall (Table 2). For May and October the number of zero values is too large to obtain reliable fits over periods of 20 years only. The inference of-the leak parameters was thus restrained to the 4 most rainy months (June, July, August, September) which still account for more than 90% of the annual total in the south and more than 95% in the north of the country.

The fit of the leak distribution was then compared with the fits of the Pearson III (two parameters) and Gaussian distributions, which means a total of 280 samples (35 stations, 4 months, 7 periods). Since the small size of the samples does not allow for a x' testing, an altemative test proposed by Brunet Moret (197s) was used for this comparison. For more than SO% of the samples the better f i t was obtained with the leak distribution, while the Pearson I I I

I

! 1

i

j MEAN NUMBER OF EVENTS MEAN NUMBER OF EVENTS

JUNE - issa to 1969 JUNE - 1970 to 1989

23 23

21 21

19 I')

17

15 I5

13

% 2 ,i? 2 17 4 --.

O ~2 4 G 8 IO 12 14 IG O 2 4 6 8 IO 12 14 16

I.onfiilrdr LlJn~llvrlu

MEAN EVENTRAINFALL (mm) JUNE -1950 to 1969

MEAN EVENT RAINFALL (mm) JUNE - 196D lo 1969

. i

55 L. Le Barbé, T. LebelfJournal of Hydrology 188-189 (1997) 43-73

distribution had a better fit on 15% of the samples. An example of the behaviour of each distribution is given in Fig. 6 for the station of Ayorou. The leak distribution has a greater ability to reproduce correctly the probability of zero rainfall, and its asymmetry is intermedi- ate between that of the Gaussian and that of the Pearson III distributions. In fact, for these three distributions, the ratio yJCV is independent of their parameters: yI/CV = O for the Gaussian distribution, y JCV = 3/2 for the leak distribution, y JCV = 2 for the Pearson III distribution. The overall better fits of the leak distribution arc an empirical confirmation of tlic suitability of this model for characterising the rainfall rcgimcs in the Sahel.

The spatial variations of the two LD parameters are shown in Fig. 7 and Fig. 8 for the months of June and August, respectively. In June both LD13[) (the mean event rainfall) and LD23" (the mean number of events) decrease when shifting from period J I to period 52.

MEAN NUMBER OF EVENTS AUGUST-I960 (0 3969

% 2 3

O 2 4 6 8 IO 12 14 16

Longitude

MEAN EVENT RAINFALL (mm) AUGUST-1960 to 1969

Longitude

MEAN NUMBER OF EVENTS AUGUST-1970 to 1989

MEAN EVENT RAINFALL (mm) AUGUST-1970 to 1989

O 2 4 G 8 10 12 14 11

Lon~iliide

Fig. S. Same as Fig. 7. escepi for Aupusr.

L. Le Barbe T. LebelfJorirnal of Hydrology 188-189 (1997) 43-73 59

However, the decrease of LD230 is remarkably well organised in space, the isolines shifting southward in a way that is very comparable to the shift of the yearly rainfall shown in Fig. 5. The changes in the LD1 map from Jl to J2 are more erratic, and smaller. In August the general pattern is similar. The LDz3,, isolines are oriented east-west and, for a given latitude, their value diminishes by 3 to 5 units between the J1 and 52 periods. In East Niger the LD13fl value is also rcduced, but by a lesser proportion than LD230. Else- where the variations of LD 13,) are negligible as compared with those of LD23". It is unclear whether this different behaviour is due to sampling effects when computing the LD parameters, or to regional differences in the consequences of the drought on the rainfall distribution. Nevertheless Fig. 8 supports globally the idea that much of the August rainfall dccrease is attributable to a n average dccrease.of 20% in the mean number of events. For half of the stations this decrease is even larger than 25%.

Thus, at the monthly scale the link between the drought and the decrease in the numher of storms emerges. We will now focus on the CSA defined in Fig. 1 to analyse the changes of rainfall climatology with finer resolution. The time resolution will be improved by considering the X parameter of the Poisson process as a continuous function of time. and the spatial resolution will increase as well, thanks to the large number of stations availnblc i n Burkina. This will also allow LIS to work on a climatically more homogeneous region hy excluding East Niger from the data set.

5. Rainfall climatology of the Central S:iliel area (1950-1989)

5. I . Corltliriorls op I l l r ~rtl~ll~.s;.s

To analyse the r:iinf;ill climatology over thc-CSA in iiiorc rlctail. two modifications I (I

the ;ipproacli taken in Section 1 are proposed. First, the stations used for each period ;ire dif'fcrcnt, i n order to t;ikc advantage of the

improvcmcnt of the nctwork over Niger during thc end of the 00s (Fig. 1). Another import;int niodilìcation is rcl;rtccl to tlic coniput:ition of' the pnramctcrs of rhc

leak tlistrihution. I n Section 4. rlic rxiiifiill process was ;issrimctl to lie ;ipproximatcly lime st:i~ioriary ;it t~ic iiiontliIy SC;II~. tlius :illowiiig t~ic tlircct iiil'crciicc of' the average niontiily I,D pxmictcrs. I-lowcvcr, tlic rcl;itivcly short duration o f the r;iiny sc;isoii, cspcci;iII\. i n lhe norll i ol' Lhe ('SA. iriiplics that the r:iinkill iii this region is strongly ilcpcndcn! on thc II'C'Z migration i ini l t1i;it the hypotlicsis ol' the monthly stxtionwity is somewhat unrcnlistic when :I niorc rlctnilcd ninlysis is undcrt;ikcn. Tlicrcforc, i t w:is tlccidcd to work on 1 I-d:iy nioviiig :ivcr;igcs i n order to ;ic'counl lor the time cvoldori ol' ¡lie paroniclcr X ol' tlic I'oisson process. I n this nictliotl the statistics :ire computed over ;I I I-rlay window ilia[ is niovccl tlxy by day. Tlic I'oisson process is considcrctl stationary over :iny I I -day period, ollow.ing l'or the coniputation of the two LD p;iranieters of that pcricxl. using thc inference ;ilgorithni Ixiscd on the cstinixtioii ol'thc number o l dry days FO. 'I'licsc two paranictcrs ;ire used ÍIS estiniates of the central day (the sixth day of the period) p;ir:imclcrs. A pair of LD parnmctcrs (LD 1, LD3) is thus computcd for ciich day, b;iscd on Ihc inforniation of the surrounding 10 days, prcitlucing il daily rcprcscntation of the LD paranietcr fluctuations over the rainy season.

I .

60 L. Le Barbé, T. LebellJolrrnal of Hydrology ISS-IS9 (1997) 43-73

SEASONAL RAINFALL (mm) 1960 to 1969 : sol ids lines 1970 to 1989 : dashed lines

Longitude COEFFICIENT OF VARIATION (%) 1960 to 1969 : solids lines 1970 to 1989: dashed lines

Longilfide

MEAN NUMBER OF EVENTS 1960 to 1969 :sol ids lines 1970 to 1989 :dashed lines

I

Longilrrde

Fig. 9. Isoline m:ips of the sessond (Ist h h y tlirough 3 Ist Oclohcr) r;liiiliill p;lranictcrs for the periods I ~ ~ ~ O - I Q ~ ~ ~ arid 1970- I9S9.

L. Le Barbé, T. LebeNJoltrnal OfHydrology I S S - I S 9 (1997) 43-73 61 QAYA (11.88 N)

DAILY MEAN NUMBER OF EUENTS

122 163 184 216 246 277 3 0 6 DIU rron tho ririt or Jmnumry

NIAMEY (13.48 N> DRILY MEAN NUMBER OF EUENTS

0 ' . . . . . i. . . : . .

122 163 164 216 246 277 308 D m u r r o m thm rirrt or J m n u m r y

AYOROU (14.76 N ) DAILY MEAN NUMBER O F EUENTS

0.6-d

i 0 ' 7 [ - 1968 - 1969 .. 1970 - 1989

0.6 - " .

QAYA (11.88 N) . MEAN EUENT RAINFALL (nm)

122 163 164 216 246 277 306 Diu rrom th. rirst OR J m n u m r y

MEAN NIAMEY EUENT RAINFALL (13.48 N) (mm)

, j :

122 163 184 216 248 277 308 0.u rrnn th. rirrt or J m n u m r y

AYOROU (14.76 N ) MEAN EUENT RAINFALL (mm)

16

I , i ~ e . - r 6 ~ " . ! . - . ,i 1978 .:...1969 .i .........

.................................................... . : 2 i ....

0 . : :

122 163 164 216 246 277 ' 5 0 8 DIU rron th- rirrt OC Jmnumry

Fig. IO. 'l'inlc 1Iuctii:itiiiii of'rhe cwnt rxinliill mid iiiciin niiniher of'cvcnts tluring t11c r;liny sc:Ison (tllree station< nf Niger over !he periods 1050- IOw) and ~WO-~WI).

. 62

5.2. The anniial raitfa11 before and after I970

L. Le Barbé, T. LebellJoiimal of Hydrology 15S-IS9 (1997) 43-73

In Fig. 5 the rainfall deficit of the years 1970-1989, in comparison with the 1950-1969 rainfall, amounts to about 100 mm in Northern Niger, increasing southward to almost 200 mm in the region of Niamey. Similar numbers are found when comparing these two periods over the CSA (Fig. 9). This confirms the extent and generality of the drought that set in at the end of the 60s. The coefficient of variation map shows that this sharp decrease of the average has been accompanied by an increase of the relative year to year variability, a fact that is not without consequences for vegetation production. The annual number of rainfall events has also been computed for each station using the following procedure. The LD distribution is fitted to the monthly rainfall distribution by the FO

DAILY MEAN NUMBER OF EVENTS 1960 -1969

.g e 2

122 184 246 308 Doy from lhe~ntoffnniiary

MEAN EVENT RAINFALL (mm) 1960-1969

DAILY MEAN NUMBER OF EVENTS 1970 -1989

l i 2 I84 246 Un.&* front theflr.yt offantior?.

MEAN EVENT RAINFALL (mm) 1970 -1989

Day front thejirsf offanrmy Dqvfrom theflrst offanrimy

Fig. I t . Space-linic dislrihuiion of Ille eveni rainkill and mean nml ler of L'V~IIIS f o r 111c periods 1950- 1969 and 1970-1989.

L. Le Barbé, T. LebelfJoiirnal of Hydrology 188-189 (1997) 43-73 63

algorithm for each of the 6 months, May to October. Summing, the monthly number of rainfall events (LD2sO parameter) yields the seasonal number of rainfall events which is niapped in Fig. 9.

The close link between the Sahelian rainfall decrease and the diminution of the number of rainfall events is confirmed. On average, the seasonal number of rainfall events has decreased by 12 to 15 units year-', while the relative decrease of both the seasonal rainfall and the mean seasonal number of events is about 25%.

5.3. Spnce-tinte flrictiiadons within h e rniny season

Six synoptic stations were selected to characterise the latitudinal rainfall gradient. Those stations are: Kandi (1 1.14"N; Benin), Gaya (1 1.SS"N; Niger), Diapaga (12.06"N; Burkina), Niamey (13.48"N; Niger), Tillabery (14.20"N; Niger), Ayorou (14.75"N; Niger). The moving window method has been applied to compute the daily LD parameters for the six stations. The results of the computation are summarised in the time charts of Fig. 10 for Gaya, Niamey and Ayorou. In the south (Gaya) tlie mean number of events (LD2) does not change much between the periods J 1 and 52. Rather, i t is the mean event rainfall (LD1) that seems to have decreased. At Kandi (not shown in Fig. IO), neither LD1 nor LD?, present any systematic change between the periods JI and 52. For all the other stations the LDT! parameter is the one that changes most between tlie two periods. The decrease of the number of events is especially important for the core of the rainy season in Diapaga and Niamey, while i t affects the whole seiison in the North (Ayorou in Fig. 11). Note that, except in Ayorou, the rainy season docs not appear to have been shortened during the dry years, a n observation olrcady made by Nicholson (1981). Regarding the mean event rainfall, no obvious pattern conies out. With the notable exception of Gaya the fluctuations are crratic, they differ from one station to another and ;dong lhe year. A sharp decrease of the mean event rainfall is observed for Niamey in Seplcinber ;ind October. A cmful an:ilysis of data from other skit ions is needed to explain this phenomenon which is observed neither at Diapaga, nor at Tillahcry nnd Ayorou, A possible numerical effect cannot be excluded at this stage.

The variations of the LD2 parameter arc of il significant niiignitudc if compared with the confidence intcrv;il of the cstimatcs. For the FO algorithm the variances of the estimates ilre givcn by the following cxprcssions:

N

& - 1 Var( LD2,) - -

N

wlicrc N is the sample size. The cocfticient of variation is thus the siime for the two estimates:

N CV(LDl,)=CV(LD2T)=

. .

(25)

(26)

(17)

. . .

3

are clearly apparent: little variation during the setting in of the rainy season; dramatic decrease of the rainfall during the core of the rainy season, with a reduction by two thirds in August, the space-time pattern of the distribution being preserved; almost no change at the end of the rainy season.

64

and the relative 90% confidence interval (C190) may be computed as 1.64 CV, or:

L. Le Barb:. T. LebellJournal of Hydrology lSS-lS9 (1997) 43-73

LDIT eLDZT-l LD27

LDl, 20.82 (-) and

since LDlT and LDzT are used as estimates of sT and AT, respectively. For T = 1 day, A, and its estimate LD2 are kept below 1.0; when LD2 = 0.5, CI90 (LD2)

= LD2 ? 0.15, and CI90 (LD1) = LD1 2 0.3LD1. For LD2 = 0.6 CI90 (LD2) = LD2 2 0.17, and Cl90 (LD1) = LD1 2 0.28LD1. While in Fig. 10 the variations of the LD1 parameter are within the limits of the 90% confidence-interval, it is clear that the 1970- 1989 values of LD? are below the lower bound of the 1950-1969 CI90 for Niamey (LD2(19Sll-196L,) = 0.6) and Ayorou (LD2~l~,Sll-19fit,) = 0.5) in August. A similar result was obtained for the three other stations (not shown). For Gaya it is quite different, the relative fluctuations of LDl being more important than those of LD2. There is no obvious explanation of this singularity.

Since the six time graphs obtained for each station arc spread niore or less regularly from south to north, it has been possible to interpolate them spatially in order to produce space- time maps for both parameters LD1 and LD2 and both periods JI and J?. These maps are given in Fig. 11. The critical disappearance of the dome characterising the LD?-Jl map in August is the most striking feature of this figure. Below 12"N the variations of LD2 are relatively small, while in the north they affect the entire period from June through mid- September. By comparison, changes in the mean event rainfall are small, with the range of 11 to 13 mm per event covering the majority of the map for both the JI and 52 periods.

31 DAY CUMULATIVE RAINFALL (mm) 31 DAY CUMULATIVE RAINFALL (mm) 1960-1969 1970-19a9

Fig. 12. Monthly r:rinf:ill ;IS ir function of time ofye:rr arid latitude for rhc pcriods lcI5O-l96O and I 07 ( )-1~ ) .

6 . The rainfall in Niamey (1905-1983)

The study of the Niamey rainfall series allows comparison of the rainfall climatology of the past 40 years with that of a longer period. It appears that, despite the particularity of the 'Joseph sequence' between 1950 and 1990, the main statistics of the series 1905-1989 and 1950- I OS9 arc similar (Tahlc 3). Behind this similarity of the global statistics, however, are hidden some important differences, which become appiirent when the period 19 10- 1989 is divided into four subperiods of 20 years ench. Using the 1 I-day moving window ;ipproacli, the LD p;iranicters hove been computcd at a daily step for each subpcriorl (Fig. 1.3 and Fig. 14). The most striking feature of these two figures is the great variability of the 1-02 curves (dtiily mc;tn numbcr ofevents) ;IS compared with th;it of the LDI curves (niemi event rainfall). The value of LDI remains bclwecn I O xiid 13 nini during the core of the rniny season (July through mid-Scptcnihcr, o r Days of year 182 to 258), for a11 four subperiods consitlcrccl, csccpt flic first otic. Intra-seasonal l1uclu:itions ilre smooth. On the contrary, both tlic pcitk atid average ol' tho LD7 parameter cli;ingc markedly from one

to ().6 during the y c m 19.30-1049 and to 0.7 in 1950-1969, bcforc diving to 0.5 during the current dry spcll ( I 970- 19SO). The intra-seasonnl fluctuation is different from that of the I-D 1 parnmctcr. The psriod of ni;isiiiiiiiii is o f I month o n l y (roughly corrcsponding to the month of August). The August ;ivcr;igc is sliglilly :iliove 0.5 for I9 IO- 1929, ~ i r o u n i l 0.55 for 1030- 1040, around 0.6 for 1050- 1009, wcll I~clow 0.5 (0.45) lor 1970- I l W .

I his masimuni is rc;iclicd progrcssivcly xitl almost 1inc;irly. st;trtirig I'rotii il low valuc ol' O. I ;it ~ h c beginning of M;ty (\vhich tiwitis the cqui\,;llcnl of otic cvcnl ill IO ~;IYs) . The post-ni;isimuni decrease is sudrlcn and rapid. l'licsc variations arc similar to tlic pttcrti of daily riiitifall itself. whicli is known to iticrc;isc slowly during the onset oftlic rainy season.

$ subpcriod to another. The peak is slightly ahovc 0.5 for the period 10 IO- 1929. I t incrcascs

-. i

I

I

i

7~:llllc 3

Skiiistics of thu Nianiuy r;iiiikill scrir3. krliics iirc' in nini l'or Ihc nican. thc' st:ind;ird dc\~i:ttion :ilid tlic I .DI pxitiickr (iilcmi cvciit r;~itiIiIl)

. 66 L. Le Barbé, T. LebellJortrnal oJHydrology 185-189 (1997) 43-73

By contrast the mean event rainfall increases rapidly between the beginning of May and June and then remains somewhat stable for almost 3 months.

Obviously, most of the rainfall fluctuations observed from one subperiod to another and within the rainy season are related to those of the mean number of events rather than to the variability of the mean event rainfall. Apart from the strong decrease of the mean number of events, one thing that may have changed during the dry spell is an earlier retreat of the rainy season: the decrease of the LD1 parameter happens 15 days earlier than during the years 1950-1969. Of course there remain sampling and numerical effects that should make one cautious when interpreting such curves. For instance, the LD1 peak of the 1910-1929 curve at the end of July, lasting for about 20 days, compensates for a hole in the LD2 curve. It is tempting to correct the hvo curves to make them more coherent with-

NIAMEY - 1910 ta 1929 MEFIN EUENT RAINFALL

122 163 184 216 246 277 386 D r y r r o m th. rirrt o r Jrnurry

NIAMEY - 1568 t o 1969 MEAN EUENT RRINFALL ( n m l

E

I

Y

DIU r r o m thæ rir-t or Jinuæry

NIAMEY - 1930 t o 1949 MEAN EUENT RAINFALL Cmml

122 163 184 216 246 277 388 Dru r r o m t h i r i r l t or JrnurrU

NIAMEY - 1978 t o 1989 MEAN EUENT RAINFALL (mm>

122 163 184 216 240 277 388 Oæy r r o m rh- rir-t or ~ænurry

Fig. 13. Time lluclualion of the event rainfill1 during Ilte rainy season (Niamey: periods I910-192Y. 3930-1949, 1950-1969 and 1970-1989).

L. Le Barb4 T. LebellJottrnal oJHydrology ISS-189 (1997) 43-73 67

those of the other periods, but we have no objective indication to guide us in doing so. Even if such a correction is made, the mean event rainfall would remain above that of the following periods. It may well be that the rainfall regime during the first quarter of the century had some significant differences from the one that prevailed later, characterised by an overall stability of the mean event rainfall during the core of the rainy season.

Consider that the July-August period accounts for about 2/3 of the total annual rainfall in Niamey. The July-August mean number of events increased by about 25% between the period 1930-1949 and the period 1950-1969 (Fig. 14). It decreased by more than 1/3 in the years 1970-1989 compared with the 1950-1969 average. Thus, the decrease in the number of rainfall events is responsible for a rainfall deficit of about 2/9 between the period 1950-1969 and the period 1970-1989, supposing (as is justified by the curves of Fig. 13) that the mean event rainfall remained unchanged. Since the overall

NIAMEY - 1918 t o 1929 DarLY ME~N NUMBER OF EUENTS

122 163 184 216 246 277 388 Dru r r o m thæ rirrt or Jmnurry

NIAMEY - 1968 t o 1969 DAILY WEAN NUMBER OF EUENTS

8 . 8 '

NIFIMEY - 1938 t o 1949

Dmy r r o m thr firit or Jmnurry

NIAMEY - 1970 t o 1989 DAILY MEFIN NUMBER OF EUENTS

............ .............. ........ ..... . . ; . I . . . . ..; .

122 163 184 210 246 277 300 Diu C r a m thæ rirmt or Jænuæry 0.y r r o m th- ririt or Jrnurry

Fig. 14. Time lluctu:ition of lhe niean nunihcr of events durin2 the rainy SC;ISOII (Ni;imey: periods 1910-1'P). 1Y30-1Y4Y. 1'150- IYOY and 1970- 19SY).

68 L. Le Barbé, T. LebellJourtral of Hydrology 188-189 (1997) 43-73

rainfall deficit is close to 25% (see Section 4) we are led to conclude that almost 90% of the rainfall deficit of the 1970-1989 years in comparison with the 1950-1969 high, has been caused by the diminution of the number of rainfall events during the core of the rainy season. Similarly the explanation of the 1950-1969 high (at least in terms of rainfall distribution) is found in the increase of the mean number of events in July and August.

Combining the analysis of the LD1 and LD2 curves, the rainy season in Niamey may be divided into three stages, the characteristics of which are given in Table 4. All the figures of this table have been crudely rounded in order to give the order of magnitudes of the contribution of each stage to the seasonal rainfall. The proportion of the July-August rainfall to the seasonal total is slightly reduced during the dsy years, which means that the rainfall deficit is larger during the core of the rainy season than on the margins. Whereas it appears possible to compute meaningful statistics on the basis of calendar months for Niamey, this may not hold for stations at higher latitudes, where the limits between the three parts of the rainy season could fall in the middle of months.

7. Validation of the model

A major asset of the leak distribution as a model of rainfall regimes is that once it has been calibrated for a given time step T, the c.d.f. of the rainfall accumulated over k time steps is still a leak distribution, assuming that an average scale parameter LD1 can be computed over the duration kT. When daily data are available it is by far preferable to choose T equal to 1 day, rather than to 10 or 30 days, in order to minimise the correlation

Table 4 Contribution of each phase of the rainy season lo the tolnl rainfall in Niamey. Riinf:iII values are in m m and the total is also given in percentage of lhe annual rainEill

1910-1929 1930-1919 I 950- 1969 1970- I9S9

May-June Mean even1 rsinfall I I 2 1.5 IO t 1.5 IO -c 1.5 IO 2 1.5 , Mean nunibur tif cvcnts 9 1 o I I 9 Total rainfall 100 (18%) I 0 0 ( I t ; % ) 1 I O ( 17%) 05 ( 1'1%)

Mean evrnl rainfdl 14% 2 11.5 -c 1.5 11.5 -c 1.5 11.5 1 1.5 Meen nuniher of cvents 27 2 3 30 -t 3 37 t J 26 C 3 Totnl rainfall 3so (67%) 350 (62%) 425 (65%) 300 (61%)

Mean event rainfdl 9.5 ? 1.5 I I -c 1.5 IO t 1.5 IO 2 1.5 Mean number of evcnts 8 9 I o 8 n o t n i rainca~~ 75 (13%) 100 (IS%) 100 (I sa) ti0 (17%)

Total r:iinfdl I O (29) I o (2%) 15 (3%) IS (3%,)

Total rainfall 565 560 650 3911

JUly-AUgUSl

September

April and Oclolxr

Rainy suawi

L. Le Barbé, T. LebellJormta[ of Hydrolop 188-189 (1997) 43-73 69

between the parameters of the leak distribution, as stated in Section 3.2. A straightforward way of independently validating the approach proposed in Section 5 is thus to compare, for a given duration of rainfall accumulation kT, the theoretical distribution derived from the daily LD parameter curves, LDl(t) and LD2(f). and the experimental distribution. This will be done below for the August daily (k = 1) and 10-day (k = 10) rainfall distributions in Niamey, for two of the subperiods studied in Section 6, that is 1950-1969 and 1970-1989. . ,

A monthly average of the LD1 parameter is first computed as a weighed mean of the 31 daily LD1 parameters of August:

where 213 and 243 are the first and last days of August, expressed as Day of year. This averaging is justified by looking at Fig. 13, where it appears that, even though the

daily LD1 parameter is affected by sampling fluctuations, these fluctuations remain around an average which does not vary much during the month of August.

The LD? parameter for a given period of August (Days i l to i?: i l + i: = k + 1) is then computed as:

712+i>

i-712 +i, LD?~,,$)= 1 LD?(i)

The model of the average daily (k = I ) rninfiill distribution for the month of August is defined by tho two following parameters:

( k - I ) LD1&j, = LDIAup

(32)

while the model of the average IO-day (k = 10) rainfall distribution is defined by the t\vo following parameters:

The theoretical dislrihutions obtained from Eqs. (2 1)-(74) arc conipiired with the experimental distributions of observed rainfall in Fig. IS. The correspondence is excellent for all four cxamplcs (daily and IO-day time steps for the wet period 1950-1969 and the dry period 1970-1989). Given that the LD curve (full line) was not fitted-to the plotted data (clots), thc similarity of the observed and computed distributions constitute a strong validation of the approach proposed here. The possibility of describing the rainfall distrihu- lions n t v:trious timc stcps by a simple two-pnrnnietcr model is thus demonstrated for tht. Sahclian rainfall.

Note that a different set o f pnranietcrs could hc computed for each of the three IO-da!

I

i

j I

I

i

70 L. Le Barbé, T. LebellJournal of Hydrology 188-189 (1997) 43-73

NIAMEY - AUGUST (1960 - 1969) DAILY RAINFALL DISTRIBUTION

4

3 m +I

"4

:2 m 3

o 1

0

0 20 40 60 80 1 0 0 DAILY RAINFALL Cmm)

NIAMEY - AUGUST ( 1 9 6 0 - 1969) 10 DAY CUMUUTIUE RAINFALL DISTRIBUTION

E. 1

1.4

0.7 "I L 2 0 L L 2-0.7

-1.4

-2.1

NIAMEY - ALIOUST (1960 -1969) MONTHLY RAINFALL OISTRI8UTION

60 100 1 6 0 200 250 3 0 0 360 Rdnrdl (mm>

NIAMEY - AUGUST (19'10 - 198B) DRILY RAINFALL DISTRIBUTION

0 20 4 0 6 0 8 0 1 8 8 DAILY RAINFALL (mn)

NIAMEY - AUQUST (1970 - 1909) 10 DRY CUMULATIUE RAINFALL DISTRIBUTIO

0 30 6 0 90 120 1 6 0 Rminr-11 (mm)

NIAMEY - AUGUST (1970 -19891 MONTHLY RAINFALL DISTRIBUTION

6 0 1 0 0 160 200 E60 3 0 0 368 R d n r - 1 1 cmml

71 L. Le Barbé, T. LebellJournal of Hydrology 18s-189 (1997) 43-73

periods (that is d l for 1-10, d2 for 11-20 and d3 for 21-31), modifying Eq. (33) as:

L D l ~ ~ ~ , = L D l A u g . (34)

for the first 10-day period of August (i would range from 1 1 to 20 for d2 and from 21 to 31 for d3).

However, the f i t of the distributions plotted in Fig. 15 to the observations is sufficiently good to assume a single 10-day distribution for all three 10-day periods of August in Niamey. The same does not necessarily hold for any other month or any other Sahelian station. In such cases the versatility of the leak distribution allows the identification of the proper set of parameters for each 10-day (or 5-day for that matter) period. It consequently provides an easy and coherent method to detect significant differences in the distribution of IO-day periods belonging to the same month.

8. Conclusion

The rainfall of the past 4 decades in the Sahel is distinguishable by the succession of 2 wet decades (1950-1969) and 7 dry decades (1970-1959), a phenomenon reminding us of the Joseph effect already noted by Mandclbrot and Wallis (1968). This paper has atteniptcd to characterise tlie rainfall climatology for each of these two periods over Cenlral Sahel. To that aim, a relatively simple stochnstic model, belonging to the compound Poisson processes family was used. This model, known :is the leak distribution. allows the decomposition of the rainfall fluctuations into two tecms: the fluctuations of the mean event rainfall, and that of the mean numher of rainfall events over any period of accumu1:ition. The model proves extremely well suited to the description of the Sahelian rainfall at a regional scale, providing a coherent set of parameters whatever the time scale considered between 1 day and 1 month. A rcmnrkiblc spatial coherence emerges from this analysis, regarding the changes

associated with the drought. AI1 over the ;irea of study (first Niger as ii whole, then the 5" x 4" region ccntrcd on tlie I-IAPEX-Sahel square), the decrease of rainfall is closely linked to a dccre;ise in the numher of rninfall cvents, escepl i n the extreme south. This decrease is especially important for the core of the rainy sewon (July, August), but in the north (14 to ISON) i t is observed over the whole rainy season. In contrast, the mean event rninf'all varies little. Thus the main change that cxplains the rainf;ill deficit of the reccnt decades clearly appears to be the number of rainfall events ratlier than tlie average strength of the rainy events o r tlie shortening of the rainy season.

Fig. 1.5. Daily (top), IO-d:iy (middle) and monthly (boltom) riiiiifiill distrihutioti i n Ni;imey for the periods 1950- 1969 (left) and 1970-198') (right). The model (full line) is a leak disrribution (LD) whose parameters \vert conipuled by averaging the ditily parameters of Figs. 13 and I I for tlie corresponding periods. Dots are the ohscrved rninhll. Although no! lilted directly IO these ohsewed reinfiills lhe LD model closely reproduces the ohserved distrihution.

72 L Le Barbé, T. LebeUJoumal of Hydrology 18S-IS9 (1997) 43-73

The fact that the length of the rainy season did not change between the wet and dry periods supports the idea that the drought is not primarily linked to a shift in the average position of the ITCZ. There is a need to identify the factor responsible for the triggering of convection (which may be a consequence of the genera1 atmospheric circulation or of local conditions), which will provide a physical basis for understanding the diminution in the number of Sahelian storms.

The consequences of this diminution in the number of rainy events, spread over a period whose length did not vary, are important for agriculture and hydrology. For instance, research on millet should probably not concentrate only on improving varieties with a short vegetative cycle but on the development of new varieties resistant to dry spells during the vegetative cycle as well. Also, the increase of the average duration between two storms in the core of the rainy season is likely to reduce the proportion of rainfall lost as surface runoff, the mean rainfall by storm being equal, because the soil has more time to dry out. This research on the rainfall regimes of West Africa is presently continuing so that it can be extended to the whole of the Sahel.

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