The Sahelian standardized rainfall index revisited

Transcription

1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 29: (2009) Published online 18 December 2008 in Wiley InterScience ( The Sahelian standardized rainfall index revisited Abdou Ali a and Thierry Lebel b * a Centre Régional AGRHYMET, BP 11011, Niamey, Niger b Laboratoire d étude des Transferts en Hydrologie et Environnement (LTHE), BP 53, IRD, Grenoble, France ABSTRACT: The Standardized Precipitation Index (SPI) is usually defined as the arithmetic mean of the normalized precipitation recorded at several stations over a region of interest where the standard deviation computed at each station over a period of reference is used as the normalizing factor. It is common to use this index in order to diagnose whether the Sahelian region can be considered as wet or dry for a given year. There are several key factors interfering with the relevance of the SPI as a measure of how rainy is a season over the Sahel. The strong spatial variability of the Sahelian rainfall at the annual scale, the uneven distribution of the raingauge network and the mean interannual climatological gradients across the region are the most important of these factors, and their influence is studied in detail here. Using an optimal interpolation algorithm to compute the SPI, the effects of various sampling schemes are first studied showing that the SPI computed as a single mean value over the whole Sahelian region is relatively robust with respect to these effects. However, the central key question remains that computing a single mean SPI over the Sahelian region hides the strong underlying spatial variability of this index. For instance, 2006 was a significantly dry season over the Sahel as a whole, but working at the resolution shows that in fact only 28% of the area was significantly dry, while 15% of the Sahel was significantly wet. From conditional empirical distributions a distribution function is proposed to determine the spatial distributions of the SPI values for a given mean regional SPI value. Studying in detail the space time pattern of the SPI over the period, also shows that recent years are characterized by a greater interannual variability than the previous 40 years, and by a contrast between the western Sahel remaining dry and the eastern Sahel returning to wetter conditions. Copyright 2008 Royal Meteorological Society KEY WORDS Sahel; rainfall index; spatial variability; drought; scale issues; decadal variability Received 29 October 2007; Revised 3 November 2008; Accepted 8 November Introduction Sahelian rainfall is notoriously unreliable and is characterized by strong interannual variability. The lasting drought of the 1970s and 1980s (see, e.g. Lamb and Peppler, 1992; Nicholson et al., 2000; Le Barbé et al., 2002) and its impact on the population and economy of the region have highlighted the importance of monitoring the Sahelian rainy season. This is usually based on a standardized precipitation index (SPI) used to quantify the wetness/dryness of a given rainy season, with respect to the climatology. The classic way of computing the SPI is to average the standardized seasonal rainfall recorded at each raingauge station available for a given year. This index is often used in a very simplistic way by assessing that the rainy season is wet if the SPI > 0, and dry if the SPI < 0. An ongoing action of the FAO (the Food and Agriculture Organisation of the UNO) is to use the SPI for insurance purposes. The FAO assigns an annual contribution to insurance companies. In return, these companies provide the FAO with the necessary funds to deal with the risks and anticipated impact of * Correspondence to: Thierry Lebel, Laboratoire d étude des Transferts en Hydrologie et Environnement (LTHE), BP 53, Grenoble Cedex 9, France. thierry.lebel@hmg.inpg.fr a drought whenever the SPI remains below a given negative threshold beyond the core of the rainy season. This simplicity of usage obviously precludes consideration of various factors that are nevertheless essential for a relevant characterization of the rainy season, such as: the method and information used to compute the index; the spatial variability of rainfall; the size and location of the study area; and the period considered to establish the reference climatology. While a few works (Katz and Glantz, 1986; Dai et al., 1997; New et al., 2001) have considered the potential influence of some of these factors, there has not yet been a comprehensive study of their effect on both the computation of the index itself and the interpretation of the value computed. There is, thus, some amount of ambiguity attached to the significance of the SPI, illustrated by recent debate on whether the severe drought of the 1970s and 1980s has ended or not (Ozer et al., 2003; Nicholson, 2005). Our study is a clear demonstration that the drought is real and is continuing, even though with en evolving pattern. The aim of this paper is, consequently, to clarify how useful and relevant the SPI might be, and what precautions are required in its interpretation. This is done by addressing two main points: (i) how robust the SPI value is when varying the method of computation and the information used (Sections 3 and 4); and (ii) how meaningful a global value Copyright 2008 Royal Meteorological Society

2 1706 A. ALI AND T. LEBEL computed over a huge area of a few millions of km 2 is, given the well known spatial variability of the Sahelian rainfall (Section 5). To introduce these questions, a brief update on the climatological conditions observed over the Sahel from 1950 to 2006 is given in Section 2, and a concluding discussion is given in the final Section A brief overview of the Sahelian rainfall climatology over the past 60 years 2.1. Data available For practical reasons of data accessibility, the Sahelian region is limited here to the area covered by the 9 Comité Inter-états de Lutte contre la Sécheresse au Sahel (CILSS) countries. The meteorological services of these countries send their raingauge data to the AGRHYMET regional centre, referred to hereafter as CRA. Because the gauge coverage is very sparse in the northern Sahel (Figure 1(a)), the study area is delimited here by latitudes 10 N and 17.5 N and by longitudes 22.5 W and 17.5 E. Over this area, the average number of available gauges is close to 600, but this number varies significantly from year to year. A more detailed description of the CRA database may be found in Ali et al. (2005). While the CRA database contains data dating as far back as 1905, most of this study focuses on the period over which the number of available stations remains continuously larger than 400 gauges. Prior to 1950, the maximum number of gauges was 187 for 1949, and the minimum number was 4 for 1915 (Figure 1(b)) Climatology The pattern of the annual rainfall is a north-to-south gradient of 1 mm/km (Lebel et al., 2003), ranging from about 100 mm at 17 N to 800 mm at 10 N (averages computed over ), with a slight decrease from west to east. The most notorious feature of the Sahelian climate is the recent drought that struck the region starting at the end of the 1960s. It is now recognized as being the most important worldwide drought of the 20th century in terms of spatial and time extension, as well as in terms of intensity, with a continuous rainfall deficit of 50% at 15 N over the period as compared to the previous period (Lebel et al., 2003). Understanding the reasons for this drought was one of the major motivations of the AMMA programme (Redelsperger et al., 2006). After 25 years of unabated drought, the first significantly wet year was recorded in 1994 (Figure 2). Since then, the situation has improved, but compared to a long-term reference starting in 1950 there have still been 8 below-average years until 2006 (Figure 2(b)). Table I summarizes, for the band encompassed between latitudes 12 N and 15 N, the decadal evolution of the mean annual rainfall, the mean daily rainfall and the mean number of rainy days (a day is considered as rainy at a gauge if it records more than 1 mm over that day) since While the mean daily rainfall remained somewhat stable (around mm), a noticeable decrease of Figure 1. The raingauge network configuration. Figure 1(a) shows the spatial configuration of the present mean number of gauges (around 600) and the synoptic network (around 80). Figure 1(b) shows the minimum and maximum year number of gauges with no missing data during the year under consideration for two periods: prior and subsequent to Prior to 1950, the minimum number of gauges is 4 for 1915 and the maximum is 187 for Subsequent to 1950, the minimum number of gauges is 232 for 2004 and the maximum is 725 for the annual cumulative rainfall (around 36%) and of the number of rainy days (around 30%) is observed when comparing the statistics of with those of Over , the determination coefficient (R 2 ) between the annual rainfall and the number of rainy days was 0.91, compared to 0.42 between the mean daily rainfall and the annual rainfall. As will be seen in Section 4, the recent years ( ) are characterized by still dry conditions in the western Sahel while the eastern Sahel benefits from wetter conditions: the ratio between the mean annual rainfall of the current period and that of the dry decade is 1.03 in the western Sahel, and 1.18 in the eastern Sahel. Before concluding this short section on the climatology of the region, it is important to draw the attention of the reader to the dependence of the SPI on the period of reference selected for the computation. An example of how sensitive our visual impression is on the reference period selected is given in Figure 2 comparing the global Sahelian SPI computed for three different periods. With respect to the longest reference period starting in 1905, the recent dry period starts in 1968, and there are only

3 THE SAHELIAN STANDARDIZED RAINFALL INDEX REVISITED 1707 interannual variability and decadal trend, linked to the number of alternate positive and negative values. To attenuate this effect it is thus proposed in the next sections to use the standard deviation of the estimation error of the regional areal rainfall as a measure of how significant is a positive (negative) SPI, when it comes to diagnose a positive (negative) anomaly of the rainy season over the Sahel. This allows a more objective assessment of the interannual and decadal variability of the Sahelian rainfall. 3. Dependence of the SPI value on the computation method Most frequently (e.g. Hulme, 1992; Lamb and Peppler, 1992; Nicholson and Palao, 1993; Le Barbé and Lebel, 1997; Nicholson et al., 2000), the SPI is computed as: SPI 1 = Ni j=1 P i j P j σ j (1) where Pj i is the rainfall of year i at station j, P j is the interannual mean rainfall at station j, σ j is the standard deviation of the annual rainfall series at station j, andn i is the number of stations of year i. In the above computation no provision is made for the spatial distribution of the stations over the study area, which is often strongly uneven. We are thus proposing to use the following alternate index here: SPI 2 = P i R P R σ R (2) Figure 2. SPI computed from different reference periods. 2(a): ; 2(b): , when the CILSS network is dense; and 2(c): , which is the OMM reference used in seasonal forecast exercises. three moderately wet years until With respect to the 57-year reference period starting in 1950, there are 3 wet years and 2 moderately wet years over the period With respect to the (which is still the WMO reference) there are 9 wet years over the period Note that the way the SPI is represented produces very contrasting visions of the where SPI 2 is the regional rainfall index of year i, PR i is the regional rainfall of year i, P R is the interannual regional rainfall average, σ R is the standard deviation of P R. Regional refers here to an areal value computed over the whole Sahelian region, as defined in Section 2.1. To minimize the effect of the uneven spatial distribution of the raingauge network used to estimate the regional rainfall, it is necessary to use some kind of optimal interpolation method (Ali et al. 2003). A comparative study of several kriging algorithms for rainfall estimation in the Sahel have led Ali et al. (2005) to select an efficient residual kriging algorithm that will be used here to compute PR i or any other areal rainfall estimate used in the paper. Table I. Evolution of the Sahelian rainfall climatology from 1950 to Values (in mm) are averages over the 12 N 15 N band. Variables Periods Annual Rainfall Mean Daily Rainfall Number of rainy days

4 1708 A. ALI AND T. LEBEL Another question regarding the application of Equation (1) is related to the network used to compute the SPI. There are 935 stations that have at least one complete year of data over the period, but there are only 37 stations that have no missing data over that period. An heuristic approach was taken to find an appropriate number of acceptable missing data in a given station series of annual totals. The SPI was computed with Equation (1) for different percentages of missing data varying from 0 to 90 with an increment of 5%, and then compared to the SPI computed with Equation (2), the latter being considered as the reference. The maximum of correlation between the two series was found when a maximum of 20% of missing data was selected: this means that over the period , a maximum of 11 annual totals is accepted to be missing at any given station for this one to be incorporated in the computation of the SPI; 273 stations satisfy this criterion forming the network used to compute the SPI when applying Equation (1). The SPI 1 series computed with Equation (1) considering this optimal threshold of 20% of missing data and the SPI 2 computed with Equation (2) are compared in Figure 3. The linear correlation between the two series is very good (r 2 = 0.984), but it can be seen that the SPI 1 series has smaller variability than the SPI 2 series. By construction, the standard deviation of the SPI 2 series is equal to 1, while the standard deviation of the SPI 1 series is that of the arithmetic average of random variables whose standard deviation is equal to 1. Except if all theses variables were perfectly correlated we know that the standard deviation of their mean is lower than the standard deviation of the individual series by a factor υ,whereν is the equivalent number of independent variables making the average. It is thus easy to re-normalize (i.e. making its standard deviation equal to 1) the SPI 1 series by dividing it by its standard deviation, and the series becomes very similar to the SPI 2 series. This means that the 273 stations network is by far sufficiently redundant to ensure a good sampling of the spatial variability over the study area, even for years where an important number of these stations are missing (115 stations for 2004). It should be noted here that another way to take into account the spatial distribution of the stations used to Figure 3. Comparison between SPI 1 computed from Equation (1), and SPI 2 computed from Equation (2). compute the SPI would be using a best linear unbiased weighting (such as kriging) of the individual SPIs computed separately at each station. One might want to use one formulation instead of the other depending on the application considered. Given the results presented further in this paper, it is clear, however, that this question is not of primary importance, a proper regionalization of the SPI being the only meaningful way to account for the rainfall patterns that may exist at the decadal scale. Of course, the number of stations used for the computation of the SPI is another important factor to consider. It is studied in the next section. 4. Dependence of the SPI value on the available information Three issues will be addressed in this section: (i) are the annual rainfall anomalies computed from the Sahelian operational network significant, taking into account the rain gauge sampling uncertainty? ii) How can the sensitivity of the SPI calculation to network density be quantified? and iii) How similar is a SPI computed on a given area (in term of size and localization) with the SPI computed on the whole Sahel? 4.1. The annual rainfall anomaly signification To answer the first question, we compare the annual rainfall anomaly to the estimation uncertainty of the regional rainfall (P R ). This estimation uncertainty is given by the standard deviation of the estimation error of the regression kriging algorithm (Ali et al., 2005) used to compute P R. The annual rainfall anomaly and the estimation uncertainty are compared in Figure 4. The positive anomalies of the period and the negative anomalies of the period are all higher than the kriging standard deviation, meaning that the continuously wet (dry) anomalies of these two periods can thus be considered and are significant from a climatological point of view. Over , only two wet years (1994 and 1999) are significant. Another significant wet period is Prior to 1922 there is almost no year where the anomaly is larger than the uncertainty, mostly because the uncertainty is very high. When considering the period as a reference for the computation of the SPI instead of the whole period remains significantly wet and significantly dry. It is, however, important to note that for 13 out of the 57 years of the period, the annual rainfall anomaly is lower (in absolute value) than the kriging standard deviation, which means that the characterization wet/dry is not certain for these years. More generally, it can be seen from Figure 4 that the kriging standard deviation (SD) is rather constant over the period, varying between 45 and 50 mm, while the anomalies vary

5 THE SAHELIAN STANDARDIZED RAINFALL INDEX REVISITED 1709 Figure 4. Comparison between the annual rainfall anomaly and the kriging standard deviation. between 200 and +200 mm, corresponding approximately to the interval [ 2; +2] for the SPI value. Taking the kriging SD as a measure of significance, we can thus roughly define a dry (resp. wet) year as a year with a SPI value lower than 0.5 (resp. higher than 0.5), corresponding to anomalies larger in absolute value than 50 mm. Remember that, at this stage, we are only considering global anomalies over the whole Sahel; thus, the values given above do not apply to SPIs computed over sub-areas Quantification of the SPI sensitivity to the number of stations The SPI was computed for networks of increasing density, by randomly sampling the total network in order to create sub-networks of N stations, N varying from 10 to 270 with a step of 10. For a given number of stations N, 50 random samplings are carried out, thus creating 50 different networks of N stations. The average correlation between the SPI computed with the N-station networks and the reference SPI computed from the total network is shown in Figure 5. The proportion of the reference SPI variability explained by the SPI computed from 10-station networks is 78%, and it becomes larger than 90% for 30-station networks. The variance explained by networks of 80 stations (equivalent to the synoptic network over our region of study), is equal to 95% on average with a maximum of 98% (obtained with the true synoptic network) and a minimum of 93%. Theoretically, the synoptic stations thus allow for an optimal estimation of the SPI over the whole Sahel. This, however, calls for two comments: (i) since not all the synoptic stations are indeed transmitted via the GTS, significant biases may appear in most real-life situations; (ii) the computation of the SPI over the whole Sahel is of little interest and significance as is shown further on in this paper and retrieving the correct pattern of decadal rainfall variability over the Sahel requires a number of raingauges far larger than the number of synoptic stations. Figure 5. Sensitivity of the SPI to the raingauge network. The graph shows the evolution of the correlation between SPI ref obtained by using all the gauges and SPI N computed using sub-networks of N stations. For each value of N, 50 different sub-networks are obtained by randomly sampling the total network. The coefficient of determination, R 2, between SPI ref and SPI N is computed for each sub-network; the average of the 50 R 2 so obtained is plotted above as the main curve. The dotted lines indicate the maximum and minimum envelope of the R 2 values. 5. Is the SPI a meaningful tool for characterizing the Sahelian rainy season? The studies presented above show the sensitivity of the SPI to the sampling carried out to compute it. This in fact results from the spatial organization of the annual Sahelian rainfields, which is characterized by a significant variability as already underlined in Ali et al. (2005). In order to study how this spatial variability impacts on the SPI, the index was computed independently over each of the boxes of the domain (754 boxes in total). This local SPI is denoted SPI 1/2 thereafter; it is used to analyse the spatial variability of the SPI Spatial distribution of the SPI The SPI 1/2 maps are first analysed on a year-byyear basis. One first striking result is that whatever the year considered globally wet or dry there are always some extremely wet or dry boxes. For example, 2006 is globally significantly dry over the region with a mean SPI equal to 0.61 (Figure 7). But SPI 1/2 varies from 2 to +2 showing very dry and very wet areas. Also 2003, which is moderately wet (mean SPI = 0.31), showed very wet and dry areas. This variability makes it difficult to state that a year is wet or dry for the entire region. However, the spatial pattern of SPI 1/2 shows some coherence, large areas being homogeneously wet or dry, as can be seen in Figure 6. Then, the mean spatial variability of SPI 1/2 is analysed for the three characteristic sub-periods of : the wet period , the dry period and the recent period For each box, the number of years when SPI 1/2 is below 0.5

6 1710 A. ALI AND T. LEBEL Figure 6. Map of SPI 1/2 for 2006; SPI 1/2 is computed by reference to the period. Figure 7. Maps of the occurrence of SPI 1/2 0.5 for three periods: ; ; and The reference period is considered for the computation of SPI 1/2. (characterizing a significant drought) is computed. This number is plotted as a percentage in Figure 7. Over the percentage of SPI 0.5 iseverywhere smaller than 5% except in the northeastern part of the Sahel, where the percentage can reach 15% locally. The percentage of SPI 0.5 is around 0% in the western part of the Sahel (Senegal area). Over , the occurrence of significant drought (SPI 0.5) is widespread over the whole region, the percentage varying between 40 and 80%. Over , the occurrence of significant drought is high in the western Sahel. This situation is in opposition to what happened during the period. The percentage of SPI 0.5 is around 60 70% in the west, 30 40% in the centre and less than 20% in the east. This period is thus characterized by two main features: (i) the west remained dry, while more humid conditions were observed in the centre and, (ii) the spatial variability and interannual variability are larger than during the previous 40 years A probabilistic interpretation of the SPI The large spatial variability of SPI 1/2 means that not all the region is dry (wet) when the mean regional SPI is negative (positive). We have thus computed the empirical distribution of the 754 SPI 1/2 values for each year i of , which produces an empirical distribution of SPI 1/2 conditional to the mean regional SPI value α i of that year, i. It is thus possible to select any given SPI 1/2 value, γ, and to compute for each year the number of boxes with a SPI 1/2 value smaller (larger) than γ. Denoting this number N(γ) SPI2=αi, the corresponding proportion is: p(γ ) SPI2=αi = ( N(γ) SPI2=αi ) / 754 (3)

7 THE SAHELIAN STANDARDIZED RAINFALL INDEX REVISITED 1711 Figure 8. Non-parametrical model fitted to the spatial distribution of the SPI 1/2 values around the regional mean value, for the threshold values 0, ±0.5, ±1. Each point corresponds to one year. The 57 values of p(γ ) SPI2=αi,(i = 1950 to 2006) are plotted in Figure 8 for a few characteristic values of γ : 1; 0, 5; 0; 0.5; 1. The resulting distributions are strongly coherent, indicating that the value of α i indeed strongly conditions the distribution of N(γ) SPI2=αi.In other words, there are some intrinsic properties of the seasonal Sahelian rainfields that are captured by SPI 2 and that can be translated into the distribution of SPI 1/2. Figure 9 provides another way of looking at these distributions. Grouping the 57 mean regional SPI values in classes of 0.1 width, the corresponding distribution of the SPI 1/2 values is computed for each class. These empirical distributions are plotted in black in Figure 9 for the following central values of the regional SPI: 1; 0, 75; 0, 5; 0, 25; 0; 0.25; 0.5; 0.75; 1. A Gaussian model was then fitted to these empirical distributions. This allows determining, for a given mean regional value of the SPI, the exceedance or nonexceedance probability to observe a given SPI 1/2 value over the region. For example, for a mean regional SPI of 0.5 (graph #3 in Fig.9) there are, in average, 51% boxes with a SPI 1/2 larger than 0.5, 21% boxes with a negative SPI 1/2 and 7% boxes that are significantly dry (SPI 1/2 smaller than 0.5). Conversely, for a mean regional SPI of 0.5 (meaning a globally significantly dry year, graph #7 in Fig.9) there are in average 8% boxes that are significantly wet (SPI 1/2 larger than 0.5) Sub-regions Several anterior studies (i.e. Nicholson, 1980; Janicot, 1992; Nicholson and Palao, 1993; Nicholson, 2005) have shown that the entire Sahel was not homogeneous with respect to rainfall variability for periods prior to 1990, and that west-east gradients are superimposed onto the more widely known north-to-south gradient. As seen above, the western Sahel is characterized by the persistence of dry conditions for years subsequent to 1994, while the eastern Sahel has seen a return to wetter conditions. This leads to the question whether a global precipitation index for the whole Sahel does make sense. The maps of Figure 7 invite to consider three separated zones in order to account for the observed average rainfall patterns of the past 15 years. In order to obtain as objective as possible a delimitation of these zones, different longitudinal limits were considered, SPI 2 being computed separately over each zone. The contrast between the three zones so obtained is quantified by computing the correlation coefficient between the SPI series (57 annual values) of each zone. The limits are set so that the contrast is maximum (i.e. when the correlation is minimum). The limit between the western Sahel and the central Sahel is found to be at 11 W in longitude (a little further west as compared to the limit of regions 1 and 2 of Janicot, 1992, and to the limit between the West Coast and the Sahel regions identified by Nicholson and Palao, 1993), while the limit between the eastern Sahel and the central Sahel is found to be at 11 E. There is a very contrasting behaviour between the eastern and western Sahel for the period after 1993, with more occurrences of wet years in the eastern Sahel, while the western Sahel remains dry (Figure 10). The probability of the eastern and the western Sahel being wet the same year is lower than 40%. Using the kriging

8 1712 A. ALI AND T. LEBEL Figure 9. Distribution of the SPI 1/2 values conditional to the regional mean value (shown for 0.1 width classes centred on 0; ±0.25; ±0.5; ±0.75; ±1). A Gaussian model is shown to fit properly all the empirical distributions. SD as a metric, it can be noticed that most of the wet years in the eastern Sahel are significant, and most of the dry years in the western Sahel are also significant. A clear recommendation stemming from this analysis is to calculate a distinct SPI for each part of the Sahel. 6. Summary and conclusion This paper deals in an exhaustive way with several key questions related to the computation of the SPI and its use to characterize the rainy season in the Sahel. This led to a few important methodological and climatological results that are summarized below Significance of the SPI value As a preliminary step, a reference method was proposed for computing the SPI from annual rainfields interpolated by an optimal residual kriging algorithm. It was shown that this method gives slightly better results than the traditional methods found in the literature in the case of irregular or under-sampling of the annual rainfields. A by-product of the method is to use the kriging SD of estimation error as a metric for assessing when the annual rainfall anomalies are significant or not. In this respect it was found that a year with a SPI value 0, 5 (>0, 5) may be deemed as significantly dry (wet). Regarding the sampling effects, the following conclusions were reached Sampling effects A network of about 40 regularly distributed stations over the whole region allows for a satisfying estimation of the global Sahelian SPI in the sense that the determination coefficient (r 2 ) between the index computed with the full

9 THE SAHELIAN STANDARDIZED RAINFALL INDEX REVISITED 1713 a SPI larger than 0.5, 21% boxes with a negative SPI and 7% boxes that are significantly dry (SPI 0.5). This is a clear indication that working at fine scale is necessary in order to apprehend correctly the rainy season. To account for this spatial variability, a probabilistic model was derived from the observations. This model gives the expected area for which the SPI is below or over a given value, conditioned to the value of the global SPI. Given the close link between rainfall deficits and crop failures in the Sahel, such a pre-determination is expected to be a useful tool for decision makers. The high spatial variability of the SPI leads us to consider that the mean SPI computed over the whole Sahel is not the appropriate tool required by the end-users for action planning in case of a prospective drought. Figure 10. Rainfall anomalies for the eastern and the western Sahel. The kriging standard deviation of estimation error is used to provide some measure of significance of the anomalies. network, and the index computed with the 40-stations network is 90%. From this result it is inferred that the synoptic network which consists of 80 stations, is a good base to estimate the SPI, even when some stations are missing, provided the optimal algorithm proposed here is used. Similarly, while the SPI computed on a 1 1 square located at the centre of the region is not representative of the SPI of the whole region, it was found that the SPI computed on a sub-domain located at the centre of the region and covering 20% of the entire Sahel (that is approximately km 2 out of an entire domain of 2.28 million km 2 ) is correlated (r 2 ) at 90% with the global Sahelian SPI A probabilistic interpretation of the mean regional SPI Sub-scale variability studies were carried out by computing yearly SPI maps over the whole region on a resolution grid; this grids contains 754 pixels. While 39% of the years of the period are evaluatedasbeing significantly dry (SPI 0.5) over the Sahel as a whole, this proportion varies from 25 to 75% at the pixel scale. The recent years ( ) display a still larger variability: while 47% of these years are characterized by a SPI 0.5 over the Sahel as a whole, this proportion varies from 15 to 90% when it is computed pixel by pixel. On average, for a mean regional SPI of 0.5 (globally significantly wet year) there are 51% boxes with 6.4. Recent climatological trends As a side result, the study carried out on the SPI at fine spatial scale highlighted that the last 15 years or so are characterized by a different pattern of variability compared to that of the previous decades. A striking fact is the higher proportion of wet years in the east and the higher proportion of dry years in the west observed over the period The existence of an eastwest gradient is clear when looking at the correlation between the SPI computed for the region located west of 11 W, on the one hand, and the SPI computed for the region located east of 11 E, on the other hand. Over the 57 years considered here, the determination coefficient, R 2, between the eastern Sahel SPI and the western Sahel SPI is equal to 57%, while it decreases to 10% over the final 14 years ( ). There is also a clear indication that the recent years are characterized by a greater interannual variability than the previous 40 years which were mainly characterized by the abrupt shift from a wet phase to a dry phase over the whole region. This is obviously food for thought and motivates research in order to explain the atmospheric dynamic factors that may explain this new space time pattern of Sahelian rainfall. Acknowledgments This research was funded by IRD and INSU in the framework of the AMMA program. Based on a French initiative, AMMA was built by an international scientific group and is currently funded by a large number of agencies, especially from France, the UK, the USA and Africa. It has been the beneficiary of a major financial contribution from the European Community s Sixth Framework Research Programme (AMMA-EU). Detailed information on scientific coordination and funding is available on the AMMA International web site, Special thanks are due to the Departement Soutien et Formation of IRD for the Grant allocated to the first-named author of this paper. We would also like to acknowledge S. Bonaventure for his efforts in the valorization of the AGRHYMET Center rainfall database, and Nick Hall for his help in proof-reading the article.

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