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The main purpose of this study is to assess the climate variability and change through statistical processing tools that able to highlight annual and monthly rainfall behavior between 1970 and 2010 in six strategical raingauges located in northern (Saint-Louis, Bakel), central (Dakar, Kaolack), and southern (Ziguinchor, Tambacounda) part of Senegal. Further, differences in sensitivity of statistical tests are also exhibited by applying several tests rather than a single one to check for one behavior. Dependency of results from statistical tests on studied sequence in time series is also shown comparing results of tests applied on two different periods (1970-2010 and 1960-2010). Therefore, between 1970 and 2010, exploratory data analysis is made to give in a visible manner a first idea on rainfall behavior. Then, Statistical characteristics such as the mean, variance, standard deviation, coefficient of variation, skewness and kurtosis are calculated. Subsequently, statistical tests are applied to all retained time series. Kendall and Spearman rank correlation tests allow verifying whether or not annual rainfall observations are independent. Hubert’s procedures of segmentation, Pettitt, Lee Heghinian and Buishand tests allow checking rainfall homogeneity. Trend is undertaken by first employing the annual and seasonal Mann-Kendall trend test, and in case of significance, magnitude of trend is calculated by Sen’s slope estimator tests. All statistical tests are applied in the period of 1960-2010. Explanatory analysis data indicates upwards trends for records in northern and central and trend free for southern records. Application of multiple tests shows that the Kendall and spearman ranks correlation tests lead to same conclusion. The difference in tests sensitivity was shown by outcomes of homogeneity tests giving different results either in dates of the shift occurrence or in the significance of an eventual shift. A synthesis analysis of results of tests was carried out to conclude about rainfall behaviors. Tests for homogeneity show that southern rainfall is homogeneous, while northern and central ones are not. According to trend test, upwards trends in Northern and central rainfall trend free in southern assumption in exploratory data analysis have been confirmed. The Sen’s slop estimator shows that all retained trend can be assumed to linear type. The same test over the period 1960-2010 shows independence of observations in all raingauges and exhibits neither trends nor breaks. This seems to show a return to a wet period.

Trend and shift detection in observed hydroclimatic records are important themes in hydrological sciences particularly in the scope of natural climate variability and potential climate change [

The concept of climate change is not simply an assumption: it has been well assessed by many reliable climate models [

Adaptation strategies to climate related consequences require financial means and a good scientific and technical development level. Many approaches can be used to assess climate change.

The first step is the exploratory analysis. Exploratory data analysis is a way to detect visually obvious trend; random behavior in hydrological time series by plotting data is plotted against time rather than testing them. This method allows selecting the appropriate hypothesis for statistical tests [

The independence between observations in rainfall time series is verified using non-parametric tests. The most tests in use for this purpose are the Pearson’s coefficient (r ), Spearman’s rho coefficient ( ρ ) or the Kendall’s coefficient ( τ ). It has been noticed that the Kendall’s tau can be an alternative to Spearman’s rho for ranked data [_{0} is tested against alternative hypothesis H_{1}.

Many scientific studies focused on checking for shifts in rainfall time series. For example, the climate variability and its impact on water resources in Grand- Lahou in Ivory Coast was analyzed using the Pettitt and Buishand tests; shifts in time series of precipitation, characterized by a diminishing of about 13% to 28% of precipitations and of about 58% of flow rates was detected around 1966 and 1981 [^{6} m^{3} per year of the volume has been noticed [

This study focuses on assessment of annual and monthly rainfall behavior through Senegal. For that, six rain gauges located in the North (Saint-Louis (SL) and Bakel (BK)), the central (Dakar (DK) and Kaolack (KL)) and the south (Ziguinchor (ZG) and Tambacounda (TC)) of Senegal have been selected. The used rainfall records cover the period from 1960 to 2010. First, the post-1970 rainfall series are analyzed in order to determine the behavior of corresponding states, and this is due to the fact that 1970 characterize the decline of precipitation in Senegal surrounding. In this period (1970-2010), exploratory data analysis involving analysis of histograms and moving average curves is made to detect obvious randomness, shift or trend in records. Furthermore, statistical characteristics such as the mean, the standard deviation, the coefficients skewness and kurtosis have been estimated. Taking into account the subjectivity of exploratory data analysis approach, statistical tests for randomness (Kendall and Spearman rank correlation tests), shift (Pettitt and Buishand tests; Lee-Heghinian and Hubert procedures) and trend (Mann-Kendall and Sen’s tests) are applied to time series. Trend tests are also applied in monthly and seasonal scale. Indeed, application of multiple tests to check for a same behavior in a time series is done on one hand for exhibiting unlikeness of tests in term of sensitivity and on one other to confirm or to reject the hypothesis to test using conclusion on the basis of majority balance sheet. Then, the same statistical tests (randomness, shift and trend) will be applied to the period from 1960 to 2010 in order to highlight the dependency of results from statistical tests on interested interval of the time series.

Senegal is located in the most extreme part West Africa between latitudes of 12˚8N - 16˚41N and longitudes of 11˚21 - 17˚32O. Its area is estimated about 196,712 km^{2}. The climate in this country is constituted by two seasons: a rainy season from June to October and a dry one from November to May. The rainy season seldom exceeds four months. Data used in this study are obtained from the database of the National Civil Aviation and Meteorological Agency of Senegal (ANACIM) and are composed by annual and monthly rainfall depth gauged in following stations: Saint-Louis (SL), Bakel (KL), Dakar (DK), Kaolack (KL), Ziguinchor (ZG) and Tambacounda (TB) in the time interval of 1960-2010. Position of exploited raingauges through the area of Senegal is shown in

Station | Station ID | Location | Data (mm) | Period of record | |
---|---|---|---|---|---|

Longitude | Latitude | ||||

Saint-Louis | 38004500 | −16.05˚ | 16.05˚ | Annual and monthly rainfall | 1970-2010 |

Bakel | 38007200 | −12.45˚ | 14.90˚ | Annual and monthly rainfall | 1970-2010 |

Dakar | 38008100 | −17.5˚ | 14.73˚ | Annual and monthly rainfall | 1970-2010 |

Kaolack | 38009700 | −16.07˚ | 14.13˚ | Annual and monthly rainfall | 1970-2010 |

Ziguinchor | 38013700 | −16.27˚ | 12.55˚ | Annual and monthly rainfall | 1970-2010 |

Tambacounda | 38011300 | −13.68˚ | 13.77˚ | Annual and monthly rainfall | 1970-2010 |

Characteristic Station | M max . TDS (˚C) | M max . TRS (˚C) | M min . TDS (˚C) | M min . TRS (˚C) | Max. TDS (%) | Max. TDS (%) | Min. TDS (%) | Min. TDS (%) | MMCEDS (mm) | MMCEDS (mm) |
---|---|---|---|---|---|---|---|---|---|---|

Saint-Louis | 31.8 | 31.9 | 17.7 | 24.2 | 81.9 | 92.7 | 34.0 | 61.3 | 5.2 | 2.9 |

Bakel | 38.2 | 36.6 | 21.9 | 24.5 | 45.3 | 85.6 | 18.6 | 46.4 | 11.2 | 11.2 |

Dakar | 26.1 | 29.9 | 19.3 | 24.6 | 90.6 | 89.9 | 55.5 | 67.7 | 3.0 | 2.5 |

Kaolack | 37.7 | 34.9 | 19.7 | 24.2 | 67.6 | 93.1 | 22.5 | 50.3 | 6.8 | 2.9 |

Ziguinchor | 36.3 | 32.8 | 20.2 | 21.5 | 88.8 | 97.1 | 30.1 | 62.1 | 3.9 | 1.6 |

In _{max} TDS and M_{max} TRS) is shown in _{min} TDS and M_{min} TRS), maximum of the air moisture during the dry and the rainy season (Max. AMDS and Max. AMRS), minimum of the air moisture during the dry and the rainy season (Min. AMDS and Min. AMDS) and mean monthly of cumulative evaporation during the dry and the rainy season (MMCEDS and MMCERS).

In this study, the first step in assessment of the rainfall behavior is exploratory data analysis. This is a graphical method in which data are plotted versus time. It allows visually checking out for randomness, shift or trend in time series observing histograms and moving average curves [

The Kendall and the Spearman rank correlation test ( [_{0} is the randomness of occurrences and significant level is fixed at 5%. We shortly describe the two tests below.

The Kendall’s rank correlation test is used to test the significance of random behavior or trend in hydroclimatic time series. It is an efficient tool for verifying linear behavior in time series, and is also referred as τ test. The Kendall’s rank correlation test is based on determining a P number of the subsequent pairs ( x i , x j ) in the time series satisfying x i < x j ( i < j ) [

τ = 4 P N ( N − 1 ) − 1 (1)

σ ( τ ) = [ 2 ( 2 n + 5 ) 9 n ( n − 1 ) ] 1 / 2 (2)

The corresponding standardized statistic Z is given by:

Z = τ σ ( τ ) (3)

The null hypothesis H 0 is accepted when Z belongs to the confident interval:

[ Z 1 − α / 2 σ ( τ ) , − Z 1 − α / 2 σ ( τ ) ] (4)

The number of observations noticed by N in the time series is first classified in ascending order. Then, the rank of each observation corresponds to its position in the classification is considered [

ρ = ( ∑ 1 N R x i R y i − ∑ 1 N R x ∑ 1 N R y i N ) ( ( ∑ 1 N R x i 2 − ( ∑ 1 N R x i ) 2 N ) ( ∑ 1 N R y i 2 − ( ∑ 1 N R y i ) 2 N ) ) (5)

If the number of the observations exceeds 10, the Student t-test can be used rather than the statistic table of Spearman. Then the statistic variable for the test is:

t = ρ ( N − 2 ) ( 1 − ρ 2 ) (6)

For α = 0.05 , the null hypothesis H 0 of randomness is accepted if | t | ≤ 2.023 .

Observations in time series are assumed to be homogeneous if all data in the times series can be considered as belonging statistically to the same population, that is that they simply follow the same statistical distribution law [_{0} is the homogeneity of the time series and the significance level is of α = 0.05 . These tests are briefly described below.

In the Hubert’s process, the time series is divided into consecutive segments m , with m > 1 and satisfying the Scheffe’s test [^{th} validate segment in the raw time series X t , the spread and the mean of corresponding segment shall be respectively:

n k = i k − i k − 1 (7)

x ¯ k = 1 n k ∑ i = i k − 1 + 1 i k x i whith i 0 = 0 (8)

For a considered series X t , segmented into sequences, the quadratic deviation, noticed by D m , is given by the formula:

D m = ∑ k = 1 m d k (9)

d k = ∑ i = i k − 1 + 1 i k ( x i − x ¯ k ) 2 (10)

An acceptable segmentation must verify the Scheffe’s test condition in which D m is constrained to be minimal and the mean of the contiguous segments x ¯ k ≠ x ¯ k + 1 significantly different.

This is a procedure of Bayesian type that is based on an assumption of a single shift in the time series. Variables are supposed in prior independence and uniformly distributed. This model project requires a consideration of following characteristics of the times series: the timing of the shift occurrence noted τ s ( 1 ≤ τ s ≤ N − 1 ) , the magnitude of the change in the mean noted δ, the mean of overall data noted by μ and the residual component that is a normal and random variable with zero mean and variance σ 2 . In this study, the approach used is only based on posterior marginal distributions of the shift position in time τ s [

x i = { μ + ε i if i = 1 , 2 , ⋯ , τ s μ + ε i + δ if i = τ s + 1 , ⋯ , N (11)

In Equation (11) ε i are fluctuations around the mean that are assumed random and normal variables with zero mean and unknown variance σ 2 . The variables μ , τ s and δ are respectively the mean, the shift timing and the magnitude of the change. Considering that the prior probability density of τ s is uniform, hence, its posterior probability will be:

P ( τ s X ) ∝ [ N τ s ( N − τ s ) ] 1 / 2 [ R ( τ s ) ] − ( N − 2 ) / 2 for ( 1 ≤ τ s ≤ N − 1 ) (12)

with

R ( τ s ) = [ ∑ i = 1 τ s ( X i − X ¯ τ s ) 2 + ∑ i = τ s + 1 N ( X i − X ¯ N − τ s ) 2 ] ∑ i = 1 N ( X i − X ¯ N ) 2 (13)

where: X ¯ N = 1 / N ∑ i = 1 N X i (Mean of the raw data); X ¯ τ s = 1 / τ s ∑ i = 1 τ s X i (Mean before date of the shift); X ¯ N − τ s = 1 / N − τ s ∑ i = τ s + 1 N X i (Mean after date of the shift).

In cases of unimodal distribution, the shift point is estimated by the mode of above marginal posterior distribution of τ s .

The Pettitt test is a nonparametric test derived from the Mann-Whitney test. It has been formulated to test homogeneity against shift in a time series [

D i , j = sgn ( x i − x j ) { 1 if ( x i − x j ) > 0 0 if ( x i − x j ) = 0 − 1 if ( x i − x j ) < 0 (14)

Then for the implementation of the statistic variable to use for the test, a basic variable U τ s , N is defined as:

U τ s , N = ∑ t = 1 τ s ∑ t = τ s + 1 N D i , j , 1 ≤ τ s ≤ N (15)

Using the theory on statistic ranks, another K N variable is derived from U τ s , N . This new variable is defined as [

K N = max | U τ s , N | ( τ s = 1 , 2 , ⋯ , N − 1 ) (16)

For the test, a probability of exceedance is fixed for a threshold value k given by the formula:

P ( K N > k ) ≅ 6 exp ( − 6 k 2 ) ( N 3 + N 2 ) (17)

The null hypothesis, H 0 is rejected if the probability of exceedance given in equation 17 is less than the significant level α for a one-sided statistic test. Hence, the shift in the time series is observed at the time τ s = t corresponding to the date of the occurrence of the retained K N .

The Buishand’s U statistic is inferred from a formulation of shift point detecting in Gardne, 1969 [

x i = { μ + ϵ i for i ∈ 0 , τ s μ + ϵ i + δ for i ∈ τ s + 1 , N (18)

where ϵ i are fluctuations around the mean that are assumed random and normal variables with zero mean and unknown variance σ 2 . In Equation (18), μ , τ and δ are the same that of define in the Lee-Heghinian test (Equation (11)). The statistic test in this approach is performed on the basis of cumulative deviation from the mean given by:

S k = ∑ i = 1 k ( x i − x ¯ ) with S 0 = 0 ; k = 1 , ⋯ , N (19)

S k is assumed to be normally distributed with zero mean. The Buishand’s U is then defined using S k and replacing the unknown variance by that of the raw data noticed by D x 2 (Equation (21)). The U is expressed as:

U = ( N ( N + 1 ) ) − 1 ∑ k = 1 N − 1 ( S k / D x ) 2 (20)

D x 2 = N − 1 ∑ i = 1 N ( X i − X ¯ ) 2 (21)

The test is made using an estimate of above unknown variance expressed in Equation (18). Estimate of the unknown is carried out to define the confident limit and is given by:

σ ^ 2 = k ( N − k ) ( N − 1 ) − 1 D x 2 , k = 0 , ⋯ , N (22)

The confidence interval that should contain the Buishand’s U if the null hypothesis is accepted is given by an ellipse of control. The function defining the ellipse is implemented employing the estimate σ ^ 2 [

± ( U 1 − α 2 k ( N − k ) ) / N − 1 D x (23)

For a given significant level α , the null hypothesis H 0 is rejected if the Buishand’s U goes out of the confidence area surrounded by the ellipse of control.

Trend tests are used in time series analysis to determine the direction of the data overall evolution in time. A declared trend indicates increasing or decreasing evolution in measured observations. It is important to highlight the fact that trend free in time series doesn’t mean a case of equality in records. These tests are used in this study to supplement the graphical approach (Exploratory Data Analysis) in which histograms moving average curves was exploited. The moving average method filters the obvious irregularities in the time series [

The moving average curve (MA) aims to filter short-term effects in time series. This approach of trend assessment involves weighting of a limited range of (2k + 1) values of the raw time series X t to transform it seems to be the most commonly used type [

Y t = 1 ( 2 k + 1 ) − 1 ∑ j = − k k X t + j (24)

The Mann-Kendall (M-K) test is use in time series analysis to detect a trend and its direction without specifying whether the trend is linear or not [

S = ∑ i = 1 N − 1 ∑ j = i + 1 N sgn ( x j − x i ) (25)

With

{ sgn ( x j − x i ) = 1 if ( x j − x i ) > 0 sgn ( x j − x i ) = 0 if ( x j − x i ) = 0 sgn ( x j − x i ) = − 1 if ( x j − x i ) < 0 (26)

A negative value of S indicates falling trend, while a positive value of the S indicates rising trend. Then, the S is assumed to be independent and normally distributed with zero mean and variance given by:

Var ( S ) = N ( N − 1 ) ( 2 N + 5 ) 18 (27)

Hence, the Z normal standard distribution of the M-K S can be defined as:

{ Z = ( S − 1 ) var ( S ) if S > 0 Z = 0 if S = 0 Z = ( S − 1 ) var ( S ) if S < 0 (28)

The null hypothesis H 0 is accepted if the P value exceeds 0.05.

In this method, for each pair of observations ( x i , x j ) an associated slope can naturally be given as:

S i , j = x j − x i j − i (29)

where x j and x i are observations at time j and i ( i < j ) respectively. In a sample of size N, the number of slopes one can obtained is given by n = N ( N − 1 ) / 2 . The Sen’s slope estimator is given by the median slope estimated after ranking the n slopes in an increasing order. If n is odd number, the median slop (MS) is given by the formula: Q [ ( n + 1 ) / 2 ] , while, if it is even by { Q n / 2 + Q [ ( n + 2 ) / 2 ] } / 2 . The null hypothesis is accepted if the estimated median slope is within the range of [ ( n − C α ) / 2 and ( n + C α ) / 2 ] , where C α = Z 1 − α 2 Var ( S ) is a standardized Gaussian statistic and α is the significance level. Var ( S ) is calculated using Equation (27), in the assumption of no tied value in the time series [

The statistical characteristics of the annual rainfall are given in

Station | Mean (mm) | Standard deviation (mm) | Coefficient of variation | Skewness | Kurtosis |
---|---|---|---|---|---|

Saint-Louis | 243.91 | 90.68 | 0.37 | 0.19 | −0.09 |

Bakel | 526.96 | 129.63 | 0.25 | 0.14 | −0.75 |

Dakar | 360.86 | 128.58 | 0.36 | 0.16 | −0.68 |

Kaolack | 582.91 | 132.57 | 0.23 | 0.65 | 0.32 |

Ziguinchor | 1208.93 | 233.89 | 0.19 | −0.09 | −0.47 |

Tambacounda | 716.80 | 175.47 | 0.24 | 0.39 | −0.74 |

Results of independency test for all times series using Kendall tau and Spearman rho tests are presented in

The results of all homogeneity tests for annual rainfall between 1970 and 2010 are presented in

Raingauge Test | Saint-Louis | Bakel | Dakar | Kaolack | Ziguinchor | Tambacounda | |
---|---|---|---|---|---|---|---|

Kendall | Kendall’s τ | 0.30 | 0.33 | 0.24 | 0.22 | 0.19 | 0.10 |

Z Statistic | 2.78 | 3.10 | 2.18 | 2.10 | 1.73 | 0.94 | |

H_{0} | Rejected | Rejected | Rejected | Rejected | Accepted | Accepted | |

Conclusion | Correlated | Correlated | Correlated | Correlated | Independent | Independent | |

Spearman | Spearman’s ρ | −0.436 | −0.438 | −0.323 | −0.321 | −0.239 | −1.151 |

Z Statistic | −3.027 | −3.042 | −2.135 | −2.119 | −1.540 | −0.953 | |

Spearman | H_{0} | Rejected | Rejected | Rejected | Rejected | Accepted | Accepted |

Conclusion | Correlated | Correlated | Correlated | Correlated | Independent | Independent |

H_{0}: Null hypothesis.

Raingauge Test | Saint-Louis | Bakel | Dakar | Kaolack | Ziguinchor | Tambacounda | |
---|---|---|---|---|---|---|---|

Hubert | H_{0} | Rejected | Rejected | Rejected | Rejected | Rejected | Rejected |

Date of shift | 1997 | 1998 | 2004 | 1998 | 2004 | 2007 | |

Pettitt | H_{0} | Rejected | Rejected | Accepted | Accepted | Accepted | Accepted |

Date of shift | 1997 | 1993 | Non shift | Non shift | Non shift | Non shift | |

Buishand | H_{0} | Rejected | Rejected | Rejected | Rejected | Accepted | Accepted |

Conclusion | Shift | Shift | Shift | Shift | Non shift | Non shift | |

L-H | Date of shift | 2009 | 1998 | 2004 | 1998 | 2007 | 2007 |

L-H: Lee-heghinian; H_{0}: Null hypothesis.

shifted. For Ziguinchor and Tambacounda, rainfall time series are assumed to be homogeneous. When H_{0} is rejected, the dates of shift occurrence often vary from a raingauge to another and also from a test to another. So, we retain as date of shift occurrence in time series, the one indicated by the maximum of tests. Thus, shift occurred at 1997 at Saint-Louis, 1998 at Bakel, and 2004 at Dakar. Zones with and without shifts in rainfall time series through the study area are shown in

Tests for trend (M-K and Sen) for all rain gauges are summarized in

Raingauge Test | Saint. Louis | Bakel | Dakar | Kaolack | Ziguinchor | Tambacounda | |
---|---|---|---|---|---|---|---|

M-K | Mann-Kendall Statistic (M-KS) | 2.77 | 3.74 | 2.17 | 2.07 | 1.92 | 1.93 |

H_{0} | Rejected | Rejected | Rejected | Rejected | Accepted | Accepted | |

conclusion | UT | UT | UT | UT | TF | TF | |

Sen’s | Median Slope (MS) | 3.21 | 4.71 | 4.27 | 7.35 | 6.48 | 2.64 |

H_{0} | Accepted | Accepted | Accepted | Accepted | Accepted | Accepted | |

conclusion | NLT | NLT | NLT | NLT | NLT | NLT |

UT: Upwards trend; NLT: Nonlinear trend; H_{0}: Null hypothesis.

The M-K test is first applied to look for trend significance. Where trend exists, Sen’s slope estimator is used to verify whether it can be considered as of a linear type, then its magnitude. The M-K test detects upwards trend (UT) for rainfall at Saint-Louis, Bakel, Dakar and Kaolack. According to the Sen’s slope estimator, existing trends are of nonlinear type (NLT). In the study area, reparation in space of studied rainfall time series with and without trend are shown in

The seasonal and monthly M-K tests are applied from 1970 to 210.

In this part of the study, we try to know how the period of study impacts the results of the test. We consider two periods of study: 1960-2010 and 1970-2010. The same tests for independency, homogeneity and trend are applied on the two periods and for all raingauges. In this section, indices of (+) is used to define acceptation of the null hypothesis and (−) for its rejection.

We compare in

Month | Observation | Statistic | Z Statistic | P value | Nulle Hypothesis |
---|---|---|---|---|---|

Station of Kaolack | |||||

Jun | 41 | 222 | 2.493 | 0.012 | Rejected |

September | 41 | 194 | 2.179 | 0.029 | Rejected |

Station of Ziguinchor | |||||

September | 41 | 183 | 2.055 | 0.040 | Rejected |

Station Variable | Saint-Louis | Bakel | Dakar | Kaolack | Ziguinchor | Tambacounda |
---|---|---|---|---|---|---|

Length (month) | 492 | 492 | 492 | 492 | 492 | 492 |

Z statistic | 0.301 | 2.530 | 1.519 | 0.161 | 1.855 | -0.049 |

P Value | 1.193 | 0.011 | 0.129 | 0.031 | 0.063 | 0.961 |

H_{0} | Accepted | Accepted | Accepted | Accepted | Accepted | Accepted |

H_{0}: Null hypothesis.

Period | 1960-2010 | 1970-2010 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Station Test | SL | BK | DK | KL | ZG | TB | SL | BK | DK | KL | ZG | TB | |

Kendall rank test | H_{0} | + | + | + | + | + | + | − | − | − | − | + | + |

conclusion | C | C | C | C | C | C | C | C | C | C | I | I | |

Spearman rank test | H_{0} | + | + | + | + | + | + | − | − | − | − | + | + |

conclusion | I | I | I | I | I | I | C | C | C | C | I | I |

C: correlated; I: independent; H_{0}: Null hypothesis; +: H_{0} accepted; −: H_{0} rejected.

of study. The period of study does not impact the results of the test for Ziguinchor and Tambacounda raingauges. We note that annual rainfall is more important for these stations.

Comparison of the test for homogeneity for the two is presented in

Period | 1960-2010 | 1970-2010 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Station Test | SL | BK | DK | KL | ZG | TB | SL | BK | DK | KL | ZG | TB | ||

Hubert | H_{0} | − | + | − | − | + | − | − | − | − | − | − | + | |

Conclusion | 1969 | H | 1969 | 1971 | H | 1966 | 1997 | 1998 | 2004 | 1998 | 2004 | 2007 | ||

Pettitt | H_{0} | + | + | + | + | − | − | − | + | + | + | + | + | |

Conclusion | H | H | H | H | H | 1975 | 1997 | 1993 | H | H | H | H | ||

Buishand | H_{0} | + | + | + | + | + | + | + | + | + | + | + | + | |

Conclusion | H | H | H | H | H | S | S | S | S | S | H | H | ||

L-H | Conclusion | 1969 | 1998 | 1969 | 1967 | 1960 | 1966 | 2009 | 1998 | 2004 | 1998 | 2007 | 2007 |

h: Homogeneous; s: shift; L-H: Lee-Heghinian; H_{0}: Null hypothesis; +: H_{0} accepted; −: H_{0} rejected.

Results of tests for trend between the two periods are compared in

Through exploratory data analysis, an overview on distribution of rainfall depth in Senegal and an assumption about upward trend in rainfall in its northern and central parts are obtained. This approach shows that rainfall depth is more important in the south and has increasing evolution in central and northern part

Period | 1960-2010 | 1970-2010 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Station Tests | SL | BK | DK | KL | ZG | TB | SL | BK | DK | KL | ZG | TB | |

M-K | H_{0} | + | + | + | + | + | + | − | − | − | − | + | + |

M-KZS | 0.32 | −0.50 | 1.04 | 0.28 | −0.66 | −0.82 | 2.77 | 3.74 | 2.17 | 2.07 | 1.92 | 1.93 | |

Conclusion | TF | TF | TF | TF | TF | TF | UT | UT | UT | UT | TF | TF | |

Sen’s | H_{0} | + | + | + | + | + | + | + | + | + | + | + | + |

MS | 0.31 | 1.44 | −1.32 | −1.42 | −3.06 | −3.06 | 3.21 | 4.71 | 4.27 | 7.35 | 6.48 | 2.64 | |

Conclusion | NLT | NLT | NLT | NLT | NLT | NLT | NLT | NLT | NLT | NLT | NLT | NLT |

TF: Trend free; UT: Upwards trend; NLT: Nonlinear trend; H_{0}: Null hypothesis; M-KZS: The M-K Z Statistic; MS: Median slope; H_{0}: Null Hypothesis; +: H_{0} Accepted; −: H_{0} rejected.

with reference to the period of 1970-2010. Descriptive statistics tools allow characterizing numerically rainfall distribution in time and space. Calculation of the means shows materialized the gradient of recorded rainfall depths in the area of Senegal. Between 1970 and 2010, rainfall gradient in space is coupled to high dispersion of observations around the means. Analysis of coefficients of variation exhibited the fact that the less the magnitudes of rainfall the higher their variability. Applied statistical tests show opposite features between rainfall in Northern and Central and those in southern, in term of independence, homogeneity and trend. They confirm that the assumed upward trends in exploratory data analysis were confirmed which randomness of rainfall was recorded in the southern part of Senegal. In addition to upward trends in northern and central, shifts were detected in related time series. Retained homogeneity hypothesis for series in southern can be considered as confirmation to their randomness feature. In monthly scale, the hypothesis of trend in the M-K test has been rejected for the same period. Therefore, results of statistical tests depend on the time series scale. Assessment of opportuneness of the time series sequence shows non-dependency of rainfall variability neither on the period nor on the geographical position. Relatively to this analysis, the high magnitude of rainfall depth from 1960 to 1970 included in the second involved period impacted the results. They have disturbed retained shift dates, inhibited confirmed upward rainfall trends and non-randomness of observations from the study focused on the period of 1970-2010. Hence, randomness tests (Kendall and Spearman ranks), if used as trend test lead to same results as the M-K one.

Ndione, D.M., Sambou, S., Sane, M.L., Kane, S., Leye, I., Tamba, S. and Cisse, M.T. (2017) Statistical Analysis for Assessing Randomness, Shift and Trend in Rainfall Time Series under Climate Variability and Change: Case of Senegal. Journal of Geoscience and Environment Protection, 5, 31-53. https://doi.org/10.4236/gep.2017.513003