Changes in rainfall regime over Burkina Faso under the climate change conditions simulated by 5 regional climate models
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Abstract
Sahelian rainfall has recorded a high variability during the last century with a significant decrease (more than 20 %) in the annual rainfall amount since 1970. Using a linear regression model, the fluctuations of the annual rainfall from the observations over Burkina Faso during 1961–2009 period are described through the changes in the characteristics of the rainy season. The methodology is then applied to simulated rainfall data produced by five regional climate models under A1B scenario over two periods: 1971–2000 as reference period and 2021–2050 as projection period. As found with other climate models, the projected change in annual rainfall for West Africa is very uncertain. However, the present study shows that some features of the impact of climate change on rainfall regime in the region are robust. The number of the low rainfall events (0.1–5 mm/d) is projected to decrease by 3 % and the number of strong rainfall events (>50 mm/d) is expected to increase by 15 % on average. In addition, the rainy season onset is projected by all models to be delayed by one week on average and a consensus exists on the lengthening of the dry spells at about 20 %. Furthermore, the simulated relationship between changed annual rainfall amounts and the number of rain days or their intensity varies strongly from one model to another and some changes do not correspond to what is observed for the rainfall variability over the last 50 years.
Keywords
Climate change Regional climate model Rainy season Multiple linear regression Sahel Burkina Faso1 Introduction
The first IPCC report on the climate change (Houghton 1990) has triggered a great interest in climate modeling in order to understand climate mechanisms and to evaluate climate evolution at short and long terms under different climate change scenarios (Nakicenovic and Swart 2000; Solomon et al. 2007; Vanvyve et al. 2008). These simulations are implemented at different spatial scales, from the global to the regional, depending on the models and the aims of the studies. However, from regional to global simulations, all climate models project a warmer climate during the 21st century (Prabhakara et al. 2000; Wu et al. 2007; Solomon et al. 2007). Other climate parameters such as rainfall are also projected to change from regional to global scale under a warming condition (Solomon et al. 2009; Wang et al. 2009).
Changes in the annual rainfall amount over the 21st century from some studies
Study  Region  Models  Scenarios  Change 

Hulme et al. (2001)  Central Sahel  CCSRNIES, CGCM1, CSIROMk2, ECHAM4, GFDLR15, HadCM2a, NCAR1  B1low, B2mid, A1mid and A2high  Significant increase 
Cook and Vizy (2006)  Sahel  CM2.1,  A2  Decrease 
MIROC3.2,  Significant increase  
CGCM2.3.2  Slight decrease  
Paeth and Hense (2004)  Sahel  ECHAM3 (coupled), ECHAM3/LSG and HADAM2  SST scenario and increase of the GHG  Slight decrease 
Mariotti et al. (2011)  West Sahel  ECHAM5 and RegCM3  A1B  Decrease 
Diallo et al. (2012)  West Sahel  ICTPRegCM3, MPIREMO, METO HCHadRM3P  A1B  Significant decrease 
SMHIRCA  Increase 
Altogether, the climate models simulations do not show any consensus in the trends of the annual rainfall amount over West African Sahel during the 21st century even when they are run under the same climate change scenario at a high spatial resolution. With a more detail on the rainy season, a study performed with a regional climate model (REMO) under two scenarios, A1B (intermediate scenario) and B1 (low scenario), Paeth et al. (2009) found a weak change in precipitation over the middle of the current century and a lengthening of dry spells within the seasons. This change of dry spells length within the rainy season despite the unchanged annual rainfall amount shows that an annual analysis of rainfall evolution can hide some changes in the internal of the rainy season that can have significant impacts on water availability and agricultural production. Furthermore, Biasutti and Sobel (2009) found another change in the evolution of the characteristics of the rainy season from the CMIP3 rainfall. They found from an analysis of monthly data, a shortening of the rainy season over Sahel with a delayed season onset of the African monsoon during the 21st century. Hence, despite these disparities and the uncertainties of the climate models (d’Orgeval et al. 2006; Déqué et al. 2007; Buser et al. 2010) in the evolution of the annual rainfall amount for the future period, a significant insight can be found on the characteristics of the rainy season. Thus, an investigation of the characteristics of the rainy season over the Sahelian region from a fine time step rainfall data is needed for a better understanding of the main changes in the rainy seasons over the future period.
On the other hand, from the observations, an analysis of the variability of rainfall regime over the region made by Le Barbé et al. (2002) and by Laux et al. (2009) showed that changes in two characteristics of the rainy season (number of rainfall events and the mean rainfall amount per event) over 1950–1990 provide an interesting results on this variability. The decrease in annual rainfall amount over the region during the last four decades (Nicholson 2005; Lebel and Ali 2009; Mahé and Paturel 2009) is characterized by a decrease in both rainfall frequency and intensity (Le Barbé et al. 2002; Balme et al. 2005) during the rainy season. However, the rainfall frequency presents the most important contribution to the annual rainfall amount variability over Sahel. The impact of the rainfall frequency (number of rain days) on the annual rainfall amount variability was highlighted by an analysis of daily rainfalls over Niger (Le Barbé and Lebel 1997). Also, crops growth and hydrological cycle depend more on rainy events organization in the rainy season than on the amount of the total rainfalls (Sivakumar 1992; Lebel and Le Barbé 1997; Vischel and Lebel 2007; Modarres 2010). Thus, an analysis of the evolution of rainfall regime over the Sahelian area from the characteristics of the rainy season better highlights the different changes in the rainfall pattern.
In this study, we analyze the evolution of rainfall regime over Burkina Faso, in West African Sahel, with regard to the changes in eight characteristics of the rainy season (date of the season onset, date of the end of season, season duration, number of rain days, mean daily rainfall, maximum daily rainfall, annual rainfall amount, and mean dry spell length). These characteristics are determined throughout a discretization procedure of the rainy season (Ibrahim et al. 2012). Indeed, the eight characteristics relate to the four main components of the rainy season: the rainy season period, the rainfall frequency and intensity and the dry spell lengths. They describe overall the potentialities of the rainy season for crops growth and runoff processes (Barron et al. 2003; Balme et al. 2006), but for this analysis we consider seven characteristics (the season duration is omitted because it comes from the date of the onset and the date of the end of season). Thus an assessment of the changes in these characteristics under the warmer conditions projected by the climate models will give a detailed insights into the overall impacts of climate changes on the rainy season. The changes in the seven characteristics of the rainy season under the climate change conditions for the IPCC A1B scenario over Burkina Faso are determined from rainfall data produced by five regional climate models (CCLM, HadRM3P, RACMO, RCA, and REMO) run over 1950–2050 period. Meanwhile, the changes in the rainy season are evaluated from a comparison between the characteristics of the rainy season over the reference period of 1971–2000 and those over the projection period of 2021–2050. For each period, a multiple linear regression model (Montgomery et al. 2001; Chen and Martin 2009) is used to describe the relationship between six characteristics of the rainy season and the annual rainfall amount. The assessment of the different relationships would highlight the most important characteristics that significantly determine the evolution of the rainfall regime. So, the regression model method is first implemented on the observed data in order to verify whether the results presented by Le Barbé et al. (2002) for the Sahel are valid for the limited area of Burkina Faso or what has changed since 1990 (last year of Le Barbé et al. (2002) analysis).
2 Data and methodology
2.1 Data and study area
References of the five regional climate models
This analysis is based on the raw data from the five simulations in order to characterize the intrinsic changes that are projected by the RCMs under the A1B scenario over Burkina Faso and other similar climatic zone. Also, the characteristics of the rainy season are determined for each station from observed and simulated daily rainfalls. However, our analyses over the whole country are based on the seasonal average value of the different characteristics over the ten stations.
2.2 Methodology
2.2.1 Definition of the characteristics of the rainy season and their variability

The season onset is determined after 5 % of the total annual rainfall amount is reached and the end of the season is determined after 95 % of the annual total rainfall amount has fallen;

The date of the season onset corresponds to the date of the rainfall higher than the average of annual first rainfall events over the entire period. In addition, to be considered, the rainfall event must not be followed by a dry spell longer than the median of the mean dry spell durations at the station or grid point;

The end of season is marked by a rainfall event occurring after or completing the 95 % of the annual rainfall amount and followed by a dry spell longer than the median dry spell duration at the station or grid point.
Meanwhile, the date of the season onset is a critical characteristic for the sowing period for food production while the second characteristic determines when the crops must reach their stage of maturity (Sivakumar 1992; Ati et al. 2002). Also, the rainy season period is delimited by the date of the season onset and the date of the end of season (the two characteristics are determined from Ibrahim et al. 2012) from which the season duration is computed. Then, the following four characteristics describe the rainfall frequency and intensity which govern soil moisture and flow intensity along the rivers. Finally, the last characteristic, the mean dry spell length, quantifies the duration of the dry period between consecutive rainfall events. Indeed, long dry spells in a rainy season can lead to crop drying out and poor harvests. Hence, characterizing the changes in these characteristics between two different periods may highlight the changes in the benefits of the rainy seasons in terms of available water resources and agronomic productions. Therefore, the significance of a change in each characteristic between the two periods is assessed with the Wilcoxon test of time series difference assessment (Ansari and Bradley 1960); for a given characteristic, the shift or difference between two periods is significant if the p value is lower than 0.05.
Furthermore, the comparison periods for the observations are determined through a statistical procedure which splits the full time series into periods of homogeneous data. The procedure is called segmentation (Hubert et al. 1989). The segmentation procedure separates the observed annual rainfall amount time series into wet and dry periods with a significant difference in the magnitude of the annual rainfall amounts for consecutive periods. The procedure is applied for the observed annual rainfall amount time series. But, for the RCMs data, we consider two periods of comparison, the reference period of 1971–2000 and the projection period of 2021–2050. Indeed the projection period is taken with regard to its climate condition which is projected to be warmer than the reference period by the climate models under the climate change condition (Hulme et al. 2001; De Wit and Stankiewicz 2006; Paeth et al. 2011).
2.2.2 Elaboration of the multiple linear regression of the annual rainfall amount

Same subsets of pertinent variables over the two periods, this implies no change in the main characteristics of the rainy season over the two periods (case 1);

The subset of the pertinent variables of one period is included in the subset of the pertinent variables of the other period; which mean that some changes in the rainy season structure may exist (case 2);

The two subsets of pertinent variables are different from one period to another, indicating a fundamental change in the structure of the rainy season (case 3).
Hence, these differences in the pertinent variables of the two regression models highlight the change in the weight of the relationship between the characteristics of the rainy season and the annual rainfall amount. The significance of the changes in the structure of the rainy season is assessed from the performance of each regression model (f _{1} and f _{2}) over the two periods. This assessment helps also to select the most representative regression model over both reference and projection periods with regard to the change in the annual rainfall amount. But, in case of the two regression models are not representative, a new regression model (f) is calibrated from the merging set of the pertinent variables over the two periods. So, if we call \( X_{1}^{*} \) the set of the pertinent variables over the reference period and \( X_{2}^{*} \) the set of the pertinent variables over the projection period, the merged pertinent variables over the two periods are \( X^{*} = X_{1}^{*} UX_{2}^{*} \). The regression model f is then elaborated from \( X^{*} \). Also, the significance of the contribution of the pertinent variables to the change in the mean annual rainfall amount is assessed from a statistical analysis performed through the regression model f.
Indeed, for two different periods (significant change in the annual rainfall amount), the regression model (f) is applied from some substitutions of the data over the first period by the data over the second period. For each pertinent variable j, its data over the first period are substituted by its randomly permuted data over the second period. The random permutation of the data is performed in order to break the interannual variability of the given variable over the second period. Thus, for each variable j, 1000 random permutations are performed in order to get a large sample of the data ranking. Then, for each variable j, the fictive projections (\( P_{1,j} \)) from f are generated and compared to (P _{2}) (main projections over the period 2021–2050 from the regression model f). Thus, variable j contributes significantly to the difference in the annual rainfall amount between the two periods if there is no significant difference between the fictive projections (P _{1,j }) and the main projections (P _{2}). In addition, an assessment from some simultaneous substitution of two or three variables is also done in case that no single substitution of the variables reproduces the change in the mean annual rainfall between the two periods. The simultaneous substitution of the variables consists in a substitution of the data of the considered variables at the same time with 1,000 random permutations of each variable.
2.2.3 Assessment of the contribution of the rainy season characteristics to the changes in the annual rainfall amount
NB: All the analyses done in this study are performed with R software (http://www.rproject.org/).
3 Historical background of rainfall variability over Burkina Faso
In this section we focus our analysis on the characteristics of the rainy season interannual variability in Burkina Faso over the 1961–2009 period. The evolution of the rainfall regime is characterized throughout the annual rainfall amount variability in order to identify significant changes that have occurred in the observed records and then their relation with the six characteristics of the rainy season.
3.1 Annual rainfall variability over the period 1961–2009
Mean values of eight characteristics of the rainy season from the observations over the three main periods
1961–1969  1970–1990  1990–2009  

Annual rainfall amount (mm/y)  895  722 (−19 %)  817 (−9 %) 
Date of the season onset (days)  12/05  21/05  16/05 
Date of the end of season (days)  30/09  28/09  30/09 
Season duration (days)  141  130 (−8 %)  137 (−3 %) 
Number of rain days (days)  53  44 (−17 %)  48 (−9 %) 
Mean daily rainfall (mm/d)  14  13 (−7 %)  13 (−7 %) 
Maximum daily rainfall (mm/d)  68  62 (−9 %)  68 
Mean dry spell length (days)  3  3  3 
On the other hand, an assessment of the changes in the characteristics between two consecutive periods shows that only the end of season and the mean dry spell length have not significantly changed between the first and the second period (Table 3). But, for the changes between the second and the third period, there is no significant change for four characteristics, the last two characteristics, the season onset and the mean daily rainfall. Altogether, in comparison with the first and the third period, the driest second period is characterized by a delayed season onset (short rainy seasons), a decrease in the number of rain days and in the intensity of the maximum daily rainfall (Table 3).
From the Stepwise procedure of pertinent variables selection for a regression model, the overall six variables were selected to elaborate the regression model (Eq. 1) over the entire observation period (1961–2009). The correlation coefficients between the six variables are lower than 0.6, which means that the six variables are not closely linked to each other. The regression model reproduces 92 % of the observed annual rainfall variance with a partial contribution of the number of rain days of 56 %, 16 % for the mean daily rainfall, 11 % for the maximum daily rainfall and the other variables contribute at less than 10 %. The multiple regression models’ projections present no significant difference with the observed annual rainfall amounts and present a correlation coefficient of about 0.9.
As verification, the Bayesian regression method (Chen and Martin 2009) was also used. It selects three pertinent variables for the regression model: the number of rain days, the mean daily rainfall and the maximum daily rainfall with a likelihood of 0.61 from a set of 10,000 iterations of the Markov Chain Monte Carlo (Gilks 1996). These three variables are also found to be dominant from the deterministic method, thus the Bayesian method confirms the relevance of these variables for the annual rainfall amount regression model. So, the multiple linear regression model built with the deterministic method is more suitable for the regression because of its simplicity and its appropriate description of the different changes in the evolution of the annual rainfall amount.
3.2 Description of the rainfall regime evolution during the period of 1961–2009
In order to compare the contribution of the changes in the various characteristics of the rainy season to the annual mean rainfall we will in the following use periods of equal length. First the predrought period (1961–1969) will be compared to the driest nine years during the drought (1977–1986). In a second step the recovery of rainfall will be examined with 19 years of the drought period (1972–1990) and the last segment of the time series with equal length (1991–2009).
3.2.1 Characterization of the annual rainfall amount decrease between 1961–1969 and 1977–1986
The three variables contribute significantly to the annual rainfall amount decrease between the two periods. From Eq. 3, we compute a contribution of 58 % due to the number of rain days, 24 % due to the mean daily rainfall and 8 % due to maximum daily rainfall. So, the three variables reproduce about 90 % of the mean shift of the annual rainfall amount between the two periods. The significant delay of the season onset (Table 3) does not contribute significantly to the decrease in the annual rainfall amount because of the low correlation between the two characteristics (−0.25). Overall, from the regression model, the number of rain days represents the main characteristic that lowered the annual rainfall amount over the second period. This characteristic has decreased by about 15 % during the second period compared with the first period. The mean daily rainfall and the maximum daily rainfall have both decreased by 8 and 9 %, respectively.
Contribution of the rainfall classes to the changes in the mean annual amount and the mean number of rain days between 1961–1969 and 1977–1986
Very low (%)  Low (%)  Moderate (%)  Strong (%)  Very strong (%)  

Rainfall amount  3  7  18  57  15 
Number of rain days  16  18  26  35  5 
3.2.2 Characterization of the annual rainfall amount increase between 1972–1990 and 1991–2009
However, from the regression model, all the six pertinent variables have contributed (Eq. 3) to the annual rainfall amount increase, with 8 % for the date of season onset, 2 % for the date of the end of the season, 60 % for the number of rain days, 6 % for the mean daily rainfall, 13 % for the maximum daily rainfall and 11 % for the mean dry spell length. So, as for the previous analysis on the description of the rainfall decrease, the number of rain days is the variable that contributes the most to the increase in the annual rainfall amount. Thus, even if the maximum daily rainfall has increased over the last period its impact on the annual rainfall amount remains lower than the impact of the number of rain days. On the other hand, the computation of the contribution of the five rainfall classes to the increase in annual rainfall (Eq. 4) shows that overall the classes between 10 and 100 mm/d contributes about 90 % to the change in the annual rainfall amount (9 % due to the mean rainfall class, 58 % due to the strong rainfall class and 23 % due to the very strong rainfall). But, for the annual number of rain days, only the very low class has significantly increased by about 25 %. The other rainfall classes frequencies display small increases in their frequencies but remain lower than those over 1961–1969 period.
The results found in this analysis of daily rainfall correspond well to those Le Barbé et al. (2002) have obtained with another method (leak distribution model) and over the entire Sahel. This confirms the ability of the multiple linear regression model to describe in more detail the evolution of the mean annual rainfall amount and the different characteristics of the rainy season. This procedure will help us to better describe the different changes in the characteristics of the rainy season projected by the five regional climate models for a warmer climate.
4 Evolution of the rainfall regime from five RCMs
Mean values of the rainy season characteristics from the observations and the five RCMs over the reference period 1971–2000
OBS  CCLM  HadRM3P  RACMO  RCA  REMO  

Annual rainfall amount (mm/y)  760  840  1160  900  670  890 
Date of the season onset (days)  138  152  105  129  121  143 
Date of the end of season (days)  272  279  292  295  271  280 
Season duration (days)  134  127  187  166  150  137 
Number of rain days (days)  46  56  144  116  61  74 
Mean daily rainfall (mm/d)  13  10.5  6.5  6  7  8 
Maximum daily rainfall (mm/d)  64  113  68  92  70  138 
Mean dry spell length (days)  3  2.5  2.5  2  2.5  2 
The whisker boxes of the annual rainfall amounts in Fig. 5 show that changes in annual rainfall between the reference and the projection period are RCM dependent. An assessment of the different changes highlights three possible cases: an increase for HadRM3P and RACMO, a decrease for CCLM and RCA, and no significant change for REMO. From this small sample it becomes evident that the influence of the driving GCM (Table 2) on the projected rainfall changes by RCMs is small as for the first two cases different lateral boundary conditions (GCM simulations) have been used (Jones et al. 1995, Mariotti et al. 2011). The increasing change concerns the two models which present the two highest mean annual rainfalls over the reference period and the decrease concerns the models which present the two lowest mean annual rainfalls over the reference period. However, the variance of the annual rainfall amounts is significantly homogeneous over the two periods for each RCM with variance ratios between 0.8 and 1.3, and a p value of FlignerKilleen test (Fligner and Killeen 1976) higher than 10 %. So, despite the significant changes in the magnitude of the annual rainfall amounts, the variance of the annual rainfall amounts has not significantly changed between the two periods. The slight increases in the variances over the projection period for CCLM, HadRM3P and RACMO (Fig. 5) are not significant. These divergences between the RCMs in the evolution of the annual rainfall amount correspond to the results of previous studies for the West African region conducted with GCMs and RCMs (Hoerling et al. 2006; Paeth et al. 2009; Biasutti and Sobel 2009). However, despite the disagreement within the CMIP3 models in the evolution of the summer time total rainfall over the 21st century, Biasutti and Sobel (2009) found a robust delay of the rainy season onset in a warmer climate. An analysis of the evolution of rainfall over Burkina Faso throughout the six main characteristics of the rainy season will better highlight the different changes in the rainfall regime even though the impacts on annual rainfall may be small or contradictory. The changes in the different characteristics of the rainy season will be evaluated with regard to the averages over the reference period presented in Table 5.
4.1 Description of the evolution of annual rainfall amount predictors
4.1.1 Rainy season start and end dates
Changes in the characteristics of the rainy season between 1971–2000 period and 2021–2050 period from the RCMs simulations
CCLM  HadRM3P  RACMO  RCA  REMO  

Date of season onset (days)  + 8.6  +0.5  +0.5  −0.3  +2.4 
Date of end of season (days)  +3.5  + 8.4  + 6.1  +5.9  +6.8 
Season duration (days)  − 7.9  +3.6  +3.0  +3.7  +0.8 
Number of rain days (days)  − 7  +0.4  +1.3  −3.1  −2.1 
Mean daily rainfall (mm/d)  +0.1  +0.6  + 0.7  −0.1  +0.3 
Maximum daily rainfall (mm/d)  −0.6  +7.8  + 19.0  −1.8  +2.1 
Average length of dry spell (days)  + 0.2  +0.1  + 0.2  +0.1  +0.1 
For the dry spell length evolution, a general consensus comes out of the five RCMs on a lengthening of the dry spells (Table 6). Two models, CCLM and RACMO CCLM and RACMO show a significant increase in the mean dry spell length of more than 5 %. The increase in the dry spell length has been found by Karambiri et al. (2011) from a different method of rainy season description. These changes in the mean dry spell length have different origins; decrease in number of rain days for CCLM while for RACMO the lengthening of the season duration is the likely cause. However, the mean dry spell length has remained stable over the observational record despite the significant changes in both rainy season duration and number of rain days.
4.1.2 Rainfall frequency and intensity
The number of rain days, the mean daily rainfall and the maximum daily rainfall allow us to better examine how the rain events change with climate. For the changes in the number of rain days (Table 6) only CCLM shows a significant decrease of around 14 % (a decrease of 6.4 days) which is in the range of the observed annual rainfall amount decrease over the two last periods (1970–1990 and 1991–2009) in comparison to the period 1961–1969. The other models only display small changes ranging from an increase of less than 1 % in HadRM3P and RACMO, and a decrease of about 3 % for RCA and REMO. In addition, we analyze the changes in the ratio of the number of rain days over rainy season length to describe how changes in the season duration impacts rainfall frequency. Altogether, there is no change in this ratio for HadRM3P and RACMO in contrast to a decrease in the ratio by 2 % for RCA and REMO and by 4 % for CCLM. Indeed, CCLM, the only model which has a significant shortening of the rainy season presents also the most important decrease in the proportion of rain days. For the mean daily rainfall (Table 6), only RACMO presents a significant change with an increase of 11 %. HadRM3P, CCLM and REMO present a slight increase of less than 6 % in contrast to RCA with a slight decrease of about 1 %. HadRM3P and RACMO display the same response with an increase in both number of rain days and mean daily rainfall while RCA shows a slight decrease in these two characteristics (Table 6). However, for CCLM and REMO a decrease in the number of rain days can be observed while the mean daily rainfall increases leading to some compensation for the annual mean rainfall (Table 6). The five RCMs present also different changes in the evolution of the maximum daily rainfall. Only RACMO present a significant increase of about 30 %. Two models, HadRM3P and REMO present a slight increase (7 and 3 % respectively) while CCLM and RCA present a slight decrease by about 2 %. Thus, the changes in the three characteristics (number of rain days, mean daily rainfall and maximum daily rainfall) taken together are different from those observed because four models show an increase in the mean daily rainfall. Only CCLM presents a decrease in both number of rain days and maximum daily rain, consistent with the change found between 1961–1969 and 1970–1990 in the observational record (Table 5).
On the other hand, the two models, CCLM and RCA, which present a decrease in the annual rainfall amount, present opposite signs in the evolution of the mean daily rainfall. In contrast, HadRM3P and RACMO with an increase in the annual rainfall amount present the same type of change over all the seven characteristics (Table 6). Altogether, some consensuses are found on a delayed end of the seasons and a lengthening of the mean dry spells. The first aspect has already been identified in GCMs (d’Orgeval et al. 2006; Biasutti and Sobel 2009).
4.2 Characterization of rainfall regime evolution from the simulations
Pertinent variables of the regression models and their contribution (in percentage) to the total variance of the annual rainfall amount
CCLM  HadRM3P  RACMO  RCA  REMO  

P1  P2  P1  P2  P1  P2  P1  P2  P1  P2  
Date of the season onset  18  x  −0.2  −0.8  −7  8  x  −1  −4  −9 
Date of the end of season  −0.8  x  −0.2  −1.2  −0.1  1  x  x  3  5 
Number of rain days  35  52  21  10  4  8  9  8  18  7 
Mean daily rainfall  42  35  76  89  93  75  89  86  73  75 
Maximum daily rainfall  x  5  x  x  8  7  x  5  5  17 
Mean dry spell length  x  x  x  0.8  x  −1  x  x  x  x 
Explained variance (%)  94  92  97  98  98  98  98  98  95  95 
Performance of the regression models from the p values of Wilcoxon test and Pearson test
CCLM  HadRM3P  RACMO  RCA  REMO  

f _{1}  f _{2}  f  f _{1}  f _{2}  f  f _{1}  f _{2}  f  f _{1}  f _{2}  f  f _{1}  f _{2}  f  
Wp value  Lv  Lv  0.92  Lv  Lv  0.74  Lv  Lv  0.95  Lv  Lv  0.73  0.3  0.3  0.94 
Pp value  Lv  Lv  <0.01  Lv  Lv  Lv  Lv  Lv  Lv  Lv  Lv  Lv  Lv  Lv  Lv 
Distribution of the changes in the annual rainfall amount within six characteristics of the rainy season for the five RCMs
CCLM  HadRM3P  RACMO  RCA  REMO  

Date of season onset (%)  −2  −0.1  −0.3  +0.04  −0.9 
Date of the end of season (%)  +0.2  +0.9  +1.1  0  +0.6 
Number of rain days (%)  −14  +0.8  +0.4  −3.6  −2.3 
Mean daily rainfall (%)  +0.3  +5.2  +8.8  −2.3  +3 
Maximum daily rainfall (%)  0  0  +1.3  0  +0.3 
Mean dry spell length (%)  0  −0.1  −0.3  0  −0.2 
Altogether, significant changes in annual rainfall amount produced by the five RCMs are dominated by changes in the number of rain days and/or the mean daily rainfall intensity. This corresponds to what has been found for the observation records as well and demonstrates that the models are able to pickup this sensitivity of the rainy season of the Sahel.
4.3 Changes in daily rainfall for different intensities
The changes in the total number of rain days and in the mean daily rainfall intensity are not homogeneously distributed over the spectrum of the rainfall intensities. These changes may concern only part of the five rainfall classes defined in the methodology. Thus, for each RCM, the variation for each rainfall class is computed relative to the average over the five rainfall classes for the reference period. The relative variation for the rainfall class k is: \( \lambda_{k} = \frac{{\Updelta Nc_{k} }}{{\overline{{N_{1} }} }}*100 \) with \( \Updelta Nc_{k} \) difference of the numbers of rain days between the two periods for rainfall class k and N _{1} average number of rain days over the reference period and a given RCM (Table 3). The same formula is used for the mean daily rainfall, with \( \Updelta Pc_{k} \) the difference of the mean daily rainfall and P _{1} the average of the mean daily for the reference period (Table 5).
Distribution (in percentage) of the changes in the number of rain days and in the mean daily rainfall among the different rainfall classes for each RCM
Number of rain days  Mean daily rainfall  

CCLM  HadRM3P  RACMO  RCA  REMO  CCLM  HadRM3P  RACMO  RCA  REMO  
Very low (%)  −7.4  −2.4  −0.6  −2.8  −1.1  −0.5  0  0  0  0 
Low (%)  −2  +0.1  +0.6  −0.7  −0.9  −0.8  0  0  0  0 
Moderate (%)  −1.4  +2  −0.1  −0.8  −0.6  −1  0  +0.1  0  +0.1 
Strong (%)  −1.3  +0.6  +0.3  −0.7  −0.5  −0.1  −0.1  +0.8  −0.1  +0.3 
Very strong (%)  −0.4  0  +1  −0.1  0.2  +35  +9.3  +11  −1.3  +3.4 
Altogether, two cases of one type of change are found with a decrease in the number of rain days over all rainfall classes for CCLM and RCA (Table 10). Thus, change in the mean values of the number of rain days and in the mean daily rainfall does not mean a single type of change over all rainfall thresholds. Also, from Tables 5 and 10 two RCMs with the same type of change in the annual rainfall amount can present different combinations of type of change over the rainfall classes. However, the only consensus that comes out from the change in the five RCMs rainfall classes is a decrease in the number of the low rainfalls (0.1–5 mm/d). The second largest change concerns four RCMs (CCLM, HadRM3P, RACMO, REMO) with an increase in the very strong rainfalls (>50 mm/d).
5 Summary
The structure of the rainy seasons is described in this study through a set of eight characteristics: date of the season onset (Onset), date of the end of season (End), season duration (SDR), number of rain days (NbRD), mean daily rainfall (MDR), maximum daily rainfall (MaxR), annual rainfall amount, and mean dry spell length (DryS). The seven characteristics address the main components of the rainy season over Sahel and allow to address properties of the rainy season more relevant for application as agricultural yields and water resources in the region. The characterization of the interannual variability of the observed and simulated rainfall over Burkina Faso is done with the multiple linear regression based on six characteristics of the rainy season (Onset, End, NbRD, MDR, MaxR, and DryS).
The linear multiple regression revealed that NbRD is the main characteristics of the rainy season that highlights the different changes in annual rainfall amount over Burkina Faso during 1961–2009 period as was found in previous studies for the Sahelian area (Le Barbé et al. 2002). However, even if MDR has decreased during the drought period, it contributes less than NbRD to the variability of the annual rainfall amounts. Also, despite the significant increase in MaxR from the period 1970–1990 to the period 1991–2009 its contribution to the increase in the annual rainfall amount over the last two decades is less important than that from NbRD. So, the increase in the very strong rainfall between the two periods is not enough to dominate the impact of the NbRD on the change in the annual rainfall amount as suggested by Lebel and Ali (2009) for the Central Sahel (11°N–17°N, 0°E–5°E). However, in contrary to Diop (1996) who did not detect a significant change in the evolution of SDR over Senegal during 1950–1991, we found that SDR has significantly decreased over Burkina Faso during the dry period 1970–1990 due to a delayed season onset. Indeed, the rainfall frequencies decrease occurs mainly at the core of the rainy season (June, July and August). On the other hand, the multiple linear regression model developed from the observations, produced a reliable representation of the rainy season over Burkina Faso which highlights the dynamics of the characteristics of the rainy season over the period of 1961–2009.
Furthermore, for the variability of the rainfall regime under the climate change condition of the A1B scenario, comparisons performed between the reference period of 1971–2000 and the projection period of 2021–2050, provide a broad range of changes in the characteristics of the rainy season across the five RCMs. The impact of climate change on annual rainfall amount over the ion period is much contrasted as in many previous studies (Dai 2006; Hulme 1994; Johns et al. 2003; Schlosser et al. 2000). Two models, CCLM and RCA project a significant decrease in annual rainfall while HadRM3P and RACMO project a significant increase in annual rainfall for the period 2021–2050. On the other hand, no significant change was found in the evolution of the annual rainfall amount for REMO between the two periods. Thus all the three possible impacts of climate change on the annual rainfall were found over Burkina Faso in these five simulations of regional climate models. This corresponds to the results of Paeth et al. (2011). They found different trends in the evolution of the annual rainfall amount over West Africa for the 21st century from a set of nine RCMs: an increase in three RCMs, a decrease in three other RCMs, and no significant trend for three other RCMs. Furthermore, in our study, only CCLM presents the same dominant variables in the annual rainfall amount decrease as found from the observations during the last five decades. This model produces also the smallest deviation in the annual rainfall amount when compared to observations. The two models, HadRM3P and RACMO, which present an increase in the annual rainfall amount over the projection period, are characterized by a significant overestimation of the annual rainfall over the reference period. This bias in the simulations of the two models which probably originate in the model’s parameterization (Ibrahim et al. 2012) can have significant impact on the models sensitivity to climate change.
However, despite the disparities in the evolution of the annual rainfall amounts for the five RCMs used in this study, a consensus was found on a delay in the end of the rainy season and an increase in the dry spell length. But these characteristics have negligible weights in the determination of the total annual rainfall. The number of rain days (NbRD) and the mean daily rainfall (MDR) are the dominant variables which explain the change in seasonal rainfall as was diagnosed by regression models for the two periods. Indeed, the decrease in annual rainfall amounts is related to a decrease in NbRD for CCLM and to a decrease in both NbRD and MDR for RCA. On the other hand, the increase in the annual rainfall amounts is related to an increase in the MDR for HadRM3P and RACMO. But changes in NbRD and in MDR are not homogeneously distributed over all five rainfall classes for most of the RCMs. Indeed, the increase in MDR for HadRM3P does not concern the strong rainfall (20–50 mm/d) and the decrease in NbRD for REMO concerns rainfalls lower than 50 mm/d. Also, four models: CCLM, HadRM3P, RACMO and REMO show an increase in the strong rainfall intensities.
6 Conclusion
The multiple linear regression models developed in this study produced a representative description of the relationships between the annual rainfall amounts and the characteristics of the rainy season which matter to applications such as agronomic yields and water resources. The methodology allowed confirming that the continuous drought condition (since 1970) over West African Sahel is characterized by a decrease in rainfall frequencies at the core of the rainy seasons (June to August).
Using climate change projections from 5 regional climate models, the methodology could prove that even though there is no consensus on the evolution of the annual rainfall amount some changes in the characteristics of the rainy season are robust through all projections. The increase in the dry spell length found in all models will be a challenge for agricultural systems (Sivakumar 1992; Laux et al. 2009) and need to be considered by countries as Burkina Faso in the adaptation plans. On the other hand, the delay in the end of the season produced by all models cannot be exploited as it is not significantly related to the total amount of rain brought by the monsoon. The changes in the main characteristics of the rainy season determining annual mean rainfall are very model dependent and thus remain difficult to exploit.
It is well known that the uncertainty in rainfall changes projected over West Africa by regional climate model is just as large as the one of global coupled atmosphere/land/ocean coupled models (Paeth et al. 2011). In our small sample of five RCMs we could not find any dependence of this uncertainty on the driving global climate model. This points towards the atmospheric component or the land surface model, as the main cause of our inability to project with confidence the changes in this monsoonal system. The parameterizations of convection have been highlighted as a source of uncertainty in previous studies (Del Genio et al. 2007; Romps 2011). The results obtained here, in particular the fact that there is little agreement between models on the changes in the characteristics of rainfall events and their synoptic variability, is a further indication that the way convection is represented in our models needs to be examined in more detail. It is thus unlikely that the uncertainty in rainfall changes projected for West Africa will decrease unless the parameterizations of convection are substantially improved (Grandpeix and Lafore 2010) or the resolution of the RCM is sufficiently high to simulate some aspects of convection explicitly.
Notes
Acknowledgments
The authors would like to thank the “Direction Nationale de la Meteorologie” of Burkina Faso for the rainfall data and the French Ministry of Foreign Affairs for the support to this study through the financial fond of “Fond de Solidarite Prioritaire”. We thank also the two anonymous reviewers for their great suggestions and comments that help to improve the quality of the paper.
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