# Statistical Assessment of Rainfall Characteristics in Upper Blue Nile Basin over the Period from 1953 to 2014

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}covering about 17% of Ethiopia. Its headwaters commence from Lake Tana at an elevation of 1830 m above sea level (asl) at Bahir Dar, as shown in Figure 1. Many tributaries join the main stream through central and southwestern Ethiopian high lands until the main stream reaches the lowlands at the Ethiopian–Sudanese border at El-Diem. The part of the Blue Nile basin in Ethiopia is called UBNB, which locates in the northwestern part of Ethiopia between longitudes 34°30′ and 39°45′ E and latitudes 7°45′ and 12°45′ N [15]. From the headwaters at Bahir Dar to down the stream at El Diem, the elevation varies from 4000 m in the headwaters in Ethiopian highlands to 480 m near the downstream at the Sudanese border with an approximate length for the Upper Blue Nile (UBN) of 940 km [1]. The basin topography is composed of hills and highlands in the northeastern part, and valleys continue in the southern and western parts [8]. Lake Tana accounts for about 7% of the UBN flow; approximately 80% of this the flow occurs between June and September, while the rest of flow occurs during March–May on the southern tributaries.

#### 2.2. Data

#### 2.3. Statistical Analysis

#### 2.3.1. Data Checking

#### 2.3.2. Variability Analysis

_{i}is the monthly rainfall in month i, and n is the number of months in the period of the considered specific season (i.e., 12 for total annual, 4 for rainy season, 3 for small rainy season, and 5 for dry season). Equation (2) proves that, for equally distributed rainfall data (same rainfall amount occurs in each month), PCI will be minimum and equal to 8.3, which corresponds to uniform distribution. A similar conclusion was made by Oliver [24] who proposed the following classification of rainfall distribution based on PCI value: PCI < 10, uniform (U); 10 < PCI ≤ 15, moderate (M); 15 < PCI ≤ 20, irregular (I); and PCI > 20, strong irregular (SI).

#### 2.3.3. Mann–Kendall Trend Test

_{o}) represents that the data series is independent and identically distributed with the insignificant trend, and it is tested against the alternative hypothesis (H

_{1}). If the null hypothesis is rejected, it indicates that the time series has either an upward or downward significant trend. The null hypothesis was tested in this study at the 5% level of significance.

_{j}and x

_{k}are sequential data values (where j > k), and the sign function sgn(x

_{j}− x

_{k}) was calculated as in Equation (4):

_{α/2}(50% of the level of confidence), then the null hypothesis (H

_{0}) is rejected. Otherwise, H

_{0}is accepted, representing that the trend is statistically insignificant. In this study, the statistical significance of the trends was evaluated at the 5% level of significance, thus a positive Z value larger than 1.96 (based on normal probability tables) indicates a significant increasing trend, while a negative Z value lower than −1.96 shows a significant decreasing trend.

#### 2.3.4. Sen’s Slope Estimator

_{i}and x

_{j}, and x

_{i}and x

_{j}are the data measurements at time i and j respectively (i > j). The positive and negative values of β indicate an upward and a downward trend in the time series, respectively [32,33,34].

#### 2.3.5. Pettitt Test for Change Point Detection

_{t}in a time series of random values {X

_{1}, X

_{2}, …, X

_{T}}, with a change point at t where F

_{1}(X) = {X

_{1}, X

_{2}, …, X

_{T}} ≠ F

_{2}(X) = {X

_{t+1}, X

_{t+2}, …, X

_{T}}.

_{0}is the absence of change point and it is tested against the alternative hypothesis H

_{a}(change point occurs, 1 ≤ t ≤ T) using the non-parametric statistic:

_{t,T}| will continue rising and no turning points will be observed. Nevertheless, when a changing point exists in the time series, |U

_{t,T}| will decrease and the turning point is formed. To determine whether change point exists or not, the probability of detecting the change point is calculated using Equation (11) considering 5% significance level, and null hypotheses H

_{0}is rejected when P is smaller than the significance level, 0.05.

## 3. Results and Discussion

#### 3.1. Descriptive Statistics and Rainfall Variability Analysis

#### 3.2. Rainfall Variability Analysis

#### 3.3. Trend Analysis of Rainfall using the Mann–Kendall Test

_{0}hypothesis (H

_{0}) and trend according to p-value, whether it exists or not (or whether it is increasing or decreasing if present).

^{−1}for Yetemen and Atnago, respectively. In contrast, the magnitude of increase for the rainy season rainfall time series was determined to be 3.33, 12.63, 11.31 and 7.25 mm year

^{−1}for Haik, Ancharo, Yetemen and Dejen, respectively. For the small rainy season in Atnago, the magnitude of decrease was determined to be −4.86 mm year

^{−1}.

#### 3.4. Detection of Change Point for Rainfall Time Series

## 4. Conclusions

^{−1}, and another three stations had an insignificant increasing trend, while only one station (Yetemen) exhibited a significant increasing rainfall trend of 12.850 mm year

^{−1}. Rainy season exhibited an insignificant decreasing trend for five stations, and an insignificant increasing trend for one station. The other four stations, Haik, Ancharo, Yetemen and Dejen, showed a significant increasing rainfall trend of 3.330, 12.650, 11.308 and 7.250 mm year

^{−1}respectively. For the small rainy season, all stations showed an insignificant decreasing trend except for Debres Markos station, which had an insignificant increasing trend. Overall, the trend analysis of the annual rainfall series indicated 40% increasing and 60% decreasing trends for the stations, while 20% of the stations had significant increasing and decreasing trends. The trend analysis of the rainy season series indicated 50% increasing and 50% decreasing trends for the stations, whereas 40% of the stations were found to have a statistically significant increasing trend over the northeastern and eastern central part of the basin. For the monthly-averaged rainfall over the basin, it was found that July and August had 45.97% of the total rainfall per year. The small rainy season contributed only 15.57% of the total rainfall per year.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The geographical location of the Upper Blue Nile Basin (UBNB) and ground rainfall stations locations. The El-Diem station, which locates in the most downstream point (i.e., the outlet) of the Upper Blue Nile Basin (UBNB), is also shown.

**Figure 4.**Amount of rainfall in the summer season contributed by each month (lines) and the coefficient of variation of rainfall in each month (bars).

**Figure 5.**Annual and seasonal Precipitation Concentration Index (PCI) values for UBNB showing PCI categories borderlines (dash-dot lines).

**Figure 6.**Time series plot for the total annual rainfall for UBNB. The dashed line indicates the Sen’s Slope trend line. Y-axis represents total annual rainfall (mm).

**Figure 7.**Time series plot for the monthly-averaged rainfall for UBNB. The dashed line indicates the Sen’s Slope trend line. Y-axis represents averaged monthly rainfall (mm).

**Figure 8.**The results for the change points assessment: (

**a**) at Bahir Dar station for the total annual rainfall, total rainfall in rainy season, and total rainfall in small rainy season; and (

**b**) at Atnago, Dejen, and Ancharo for the total annual rainfall. The dashed lines represent the mean of time series before and after the changing point.

**Table 1.**Geographic characteristics of the rainfall stations and descriptive statistics for the rainfall data time.

Station | Zone Location | Coordinates | Missing Data (%) | Period of Record for Rainfall Data | |||
---|---|---|---|---|---|---|---|

Latitude (°N) | Longitude (°E) | Elevation (asl) (m) | |||||

1 | Gondar AP | Northern | 12.52 | 37.43 | 2000 | 6 | 1953–2014 |

2 | Bahir Dar | Northern | 11.36 | 37.24 | 1770 | 13 | 1961–2014 |

3 | Ancharo | Northeastern | 11.05 | 39.78 | 2235 | 18 | 1957–2013 |

4 | Combolcha | Northeastern | 11.08 | 39.71 | 1862 | 3 | 1953–2013 |

5 | Haik | Northeastern | 11.31 | 39.68 | 2081 | 0 | 1957–2013 |

6 | Chagni | Central | 10.97 | 36.50 | 1608 | 16 | 1974–1990 /1999–2014 |

7 | Debre Markos | Central | 10.33 | 37.74 | 2515 | 7 | 1954–2012 |

8 | Yetemen | Eastern central | 10.33 | 38.15 | 2394 | 8 | 1976–2013 |

9 | Dejen | Eastern central | 10.17 | 38.15 | 2222 | 0 | 1972–2014 |

10 | Atnago | Southwestern | 8.1 | 34.35 | 503 | 5 | 1969–1977 /1980–2010 |

**Table 2.**Summary results of Mann–Kendall trend analysis for total annual and seasonal rainfall data.

Station | Gondar AP | Bahir Dar | Combolcha | Haik | Ancharo | Chagni | Debres Markos | Yetemen | Dejen | Atnago | |
---|---|---|---|---|---|---|---|---|---|---|---|

Zone location | N | N | NE | NE | NE | C | C | EC | EC | SW | |

Total Annual | τ | −0.047 | −0.156 | −0.088 | 0.021 | 0.11 | −0.108 | −0.018 | 0.327 | 0.205 | −0.292 |

S | −75 | −161 | −145 | 23 | 58 | −47 | −28 | 162 | 168 | −205 | |

p-value | 0.6 | 0.13 | 0.334 | 0.84 | 0.377 | 0.412 | 0.849 | 0.009 | 0.061 | 0.01 | |

Z | −0.51 | −1.51 | −0.97 | 0.20 | 0.88 | −0.82 | −0.19 | 2.61 | 1.88 | −2.56 | |

Sen’s S | −1.084 | −4.36 | −1.33 | 0.541 | 3.661 | −4.408 | −0.307 | 12.85 | 5.938 | −17.73 | |

H_{0} | A | A | A | A | A | A | A | R | A | R | |

Trend | I | I | I | I | I | I | I | S (↑) | I | S (↓) | |

Rainy Season | τ | −0.039 | −0.167 | 0.054 | 0.217 | 0.371 | −0.122 | −0.016 | 0.343 | 0.271 | −0.209 |

S | −62 | −173 | 89 | 235 | 196 | −53 | −24 | 170 | 222 | −147 | |

p-value | 0.675 | 0.103 | 0.555 | 0.032 | 0.003 | 0.354 | 0.871 | 0.006 | 0.013 | 0.066 | |

Z | −0.42 | −1.63 | 0.59 | 2.15 | 3.02 | −0.93 | −0.16 | 2.74 | 2.48 | −.84 | |

Sen’s S | −0.628 | −4.124 | 0.67 | 3.33 | 12.625 | −4.267 | −0.159 | 11.308 | 7.25 | −11.53 | |

H_{0} | A | A | A | R | R | A | A | R | R | A | |

Trend | I | I | I | S (↑) | S (↑) | I | I | S (↑) | S (↑) | I | |

Small Rainy Season | τ | −0.057 | 0.027 | −0.007 | −0.079 | −0.125 | −0.007 | 0.036 | −0.119 | −0.039 | −0.231 |

S | −91 | 28 | −12 | −85 | −66 | −3 | 56 | −59 | −36 | −162 | |

p-value | 0.536 | 0.798 | 0.947 | 0.441 | 0.314 | 0.972 | 0.697 | 0.347 | 0.728 | 0.043 | |

Z | −0.62 | 0.26 | −0.07 | −.77 | −1.00 | −0.04 | 0.39 | −0.94 | −0.35 | −2.02 | |

Sen’s S | −0.38 | 0.182 | −0.07 | −1.154 | −2.741 | −0.057 | 0.235 | −1.689 | −0.476 | −4.862 | |

H_{0} | A | A | A | A | A | A | A | A | A | R | |

Trend | I | I | I | I | I | I | I | I | I | S (↓) | |

Dry Season | τ | −0.075 | −0.167 | −0.119 | −0.129 | −0.178 | −0.14 | −0.066 | −0.016 | 0.029 | 0.013 |

S | −120 | −173 | −197 | −139 | −94 | −61 | −102 | −8 | 24 | 9 | |

p-value | 0.413 | 0.103 | 0.189 | 0.206 | 0.15 | 0.284 | 0.475 | 0.9 | 0.796 | 0.92 | |

Z | −0.82 | −1.63 | −1.31 | −1.27 | −1.44 | −1.07 | −0.71 | −0.11 | 0.26 | 0.10 | |

Sen’s S | −0.261 | −1.132 | −0.645 | −1.32 | −2.966 | −2.236 | −0.508 | −0.244 | 0.387 | 0.143 | |

H_{0} | A | A | A | A | A | A | A | A | A | A | |

Trend | I | I | I | I | I | I | I | I | I | I |

^{*}The bold-type p-values are smaller than 0.05; A, accepted; R, rejected; I, insignificant trend; S, significant trend.

**Table 3.**Summary results of Mann–Kendall trend analysis for monthly-averaged rainfall over the UBNB.

Jan. | Feb. | Mar. | April | May | June | July | Aug. | Sep. | Oct. | Nov. | Dec. | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

τ | −0.052 | −0.239 | 0.050 | −0.063 | 0.192 | 0.303 | −0.169 | 0.062 | 0.136 | 0.225 | 0.036 | −0.094 |

S | −99 | −452 | 95 | −119 | 363 | 573 | −319 | 117 | 257 | 425 | 69 | −177 |

p-value | 0.547 | 0.006 | 0.564 | 0.470 | 0.027 | 0.001 | 0.053 | 0.477 | 0.119 | 0.010 | 0.675 | 0.282 |

Z | −0.595 | −2.739 | 0.571 | −0.717 | 2.199 | 3.474 | −1.932 | 0.705 | 1.555 | 2.575 | 0.413 | −1.070 |

Sen’s S | −0.054 | −0.370 | 0.135 | −0.205 | 0.821 | 1.279 | −0.755 | 0.265 | 0.475 | 0.855 | 0.039 | −0.094 |

H_{0} | A | R | A | A | R | R | A | A | A | R | A | A |

Trend | I | S (↓) | I | I | S (↑) | S (↑) | I | I | I | S (↑) | I | I |

% sharing | 1.24 | 1.75 | 3.62 | 4.61 | 7.34 | 12.05 | 23.32 | 22.65 | 13.90 | 6.49 | 1.92 | 1.09 |

^{*}The bold-type p-values are smaller than 0.05; A, accepted; R, rejected; I, insignificant trend; S, significant trend.

**Table 4.**Summarized results of Pettitt test for the total annual and seasonal rainfall time series

^{a}.

Total Annual Rainfall | Rainy Season Rainfall | Small Rainy Season Rainfall | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Year of Change Point | Mean before Change Point | Mean after Change Point | Percent of Change | Year of Change Point | Mean before Change Point | Mean after Change Point | Percent of Change | Year of Change Point | Mean before Change Point | Mean after Change Point | Percent of Change | |

Bahir Dar | 1977 (−) | 1552 | 1279 | 17.6 | 1977 (−) | 1305 | 1074 | 17.7 | 1974 (−) | 136 | 106 | 22.1 |

Ancharo | - | - | - | - | 1997 (+) | 605 | 854 | 41.1 | - | - | - | - |

Dejen | - | - | - | - | 1987 (+) | 837 | 1055 | 25.98 | - | - | - | - |

Atnago | 1982 (−) | 2210 | 1533 | 30.6 | 1977 (−) | 1629 | 1019 | 37.4 | - | - | - | - |

^{*}The positive signs in the parentheses indicate increasing shift and negative signs indicate decreasing shift.

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**MDPI and ACS Style**

Samy, A.; G. Ibrahim, M.; Mahmod, W.E.; Fujii, M.; Eltawil, A.; Daoud, W.
Statistical Assessment of Rainfall Characteristics in Upper Blue Nile Basin over the Period from 1953 to 2014. *Water* **2019**, *11*, 468.
https://doi.org/10.3390/w11030468

**AMA Style**

Samy A, G. Ibrahim M, Mahmod WE, Fujii M, Eltawil A, Daoud W.
Statistical Assessment of Rainfall Characteristics in Upper Blue Nile Basin over the Period from 1953 to 2014. *Water*. 2019; 11(3):468.
https://doi.org/10.3390/w11030468

**Chicago/Turabian Style**

Samy, Abeer, Mona G. Ibrahim, Wael Elham Mahmod, Manabu Fujii, Amr Eltawil, and Waled Daoud.
2019. "Statistical Assessment of Rainfall Characteristics in Upper Blue Nile Basin over the Period from 1953 to 2014" *Water* 11, no. 3: 468.
https://doi.org/10.3390/w11030468