Temporal Dynamics and Trend Analysis of Areal Rainfall in Muger Subwatershed, Upper Blue Nile, Ethiopia

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Introduction
Rainfall is one of the most important variables that afect both the spatial and temporal availability of fresh water in specifc regions [1].Variability of rainfall infuences waterdependent activities of human beings especially rain-fed agricultural activity [2][3][4][5].Nowadays, examining the variability and trends of weather over space and time is becoming an area of serious concern.Previous studies conducted on climate variability, for example, Larbi et al. [6], Taxak et al. [7], Asfaw et al. [8], Miheretu [9], Adugna et al. [10], Kale and Nagesh Kumar [11], Bekuma et al. [12], Hussain et al. [13], Birara et al. [14], Ma et al. [15], Serrano-Notivoli et al. [16], and Takano-Rojas et al. [17] stated the signifcances of serious examination and monitoring of potential impacts and planning of possible adaptation strategies in diferent sectors.Moreover, Duan et al. [18] studied the annual, seasonal, and monthly precipitation trends for the northern Japanese Island of Hokkaido using the Mann-Kendall test and geostatistical interpolation techniques.Tis study revealed that most stations are with declining trends and among these, almost all of the stations showed increasing trends in May and July.Another study provides insight into the most refned trend on monsoon rainfall at different spatial scales in India using a multimethod approach consisting of the linear regression model (LRM), Mann-Kendall test (MKT), and innovative trend analysis (ITA) analyzed in particular and synchronized way [19].Additionally modifed Mann-Kendall's test, Sen's slope test, Weibull's recurrence interval, Pearson's coefcient of skewness, consecutive disparity index, and kurtosis are included to evaluate the trends of the West Coast Plain and Hill Agroclimatic Region of India [20].
Mann-Kendall's and Sen's slope tests are the most widely applied approaches used for trend analysis in diferent parts of the world [21][22][23].
Rainfall in Ethiopia shows high variability across space and time [24][25][26].It is characterized by wet and long rainy seasons on the one hand and dry and short rainy seasons on the other hand.Consequently, the high and low rainfall phenomena can give rise, respectively, to food and drought conditions with adverse economic and humanitarian crises [27].In Ethiopia, agricultural practice is dependent on rainfall [10,12,24,28].
Tere are three seasons in Ethiopia.Tese are the June-September (main rainy season, locally known as Kiremt); the March-May (short rainy season, locally known as Belg); and the October-February (dry season, locally known as Bega) [29].Understanding the characteristics of Kiremt and Belg season rainfall is important to improving agricultural productivity and mitigating food security challenges and water resource development of the country.Belg and Bega seasons rainfall are more variable than that of Kiremt rainfall which is the largest in terms of its amount and geographical coverage.Terefore, the Belg season crops and the food security of households may highly be afected by high temporal and spatial variability of Belg season rainfall.Kiremt season rainfall supports the main cropping season production, locally known as Meher.Te change and shift in Belg season rainfall led to devastating droughts afecting socioeconomic welfare and environmental resources.
Various scholars conduct a trend analysis of rainfall for single or group stations on a local and regional level.Terefore, monthly, seasonal, and annual variability and trend analysis of rainfall is not new in Ethiopia.However, most of these studies are considering the point of rainfall.Te main objective of this study was to evaluate seasonal and annual variability and trend analysis of areal rainfall recorded in the last 40 years (1980-2019) in the Muger subwatershed.
Te altitude of the study subwatershed ranges from 975 m to 3534 m asl.Te average annual rainfall gauged in the Muger subwatershed ranged from 1099.6 mm at Fiche station to 1536 mm at Chancho station.Te socioeconomic activity of the society in this subwatershed depends on rainfed agriculture during the period from April to September.Te climate of the study area is characterized by three seasons, October-February is named winter (Bega), March-May is named spring (Belg), and the summer (Kiremt) season is extended from June-September.

Data Source.
Te rainfall data for variability and trend analysis have been obtained from Ethiopian National Meteorology Agency from 1980 to 2019.Furthermore, the feature of meteorology stations is elaborated on in Table 1.
Te abovementioned gauge stations give the point rainfall in and around Muger subwatershed but to assess the temporal dynamics and trend analysis as a subwatershed areal rainfall was required.Various applications in hydrology require an understanding of the spatial and temporal behavior of extreme rainfall over a catchment as it impacts the runof behavior and its scaling characteristics [30].In engineering practice, point rainfall intensity is only applicable to very small catchments, as already pointed out by Breinl et al. [31].For this reason, areal reduction factors (ARFs) are applied to transform point rainfall into areal rainfall.Te areal rainfall of the study subwatershed was determined in the geographical information system (GIS) by the Tiessen polygon method using the equation suggested by Pande [32].
where P avr is the areal average precipitation, P i is the point precipitation of the i th station, A i is the area of contribution of the i th station, and n is the number of meteorology stations.Te contribution area of gauging stations in the Muger subwatershed is indicated in Figure 2.

Temporal Dynamics Analysis.
Rainfall in a specifc region may vary in its frequency, pattern, and distribution through a time named as temporal dynamics of rainfall [8,9,33,34].Tere are various methods to check this variability which include the standardized anomaly index (SAI) to analyze the frequency and intensity of the precipitation, the coefcient of variation (CV) to estimate the seasonal and annual rainfall variation pattern, and the precipitation concentration index (PCI) to evaluate the distribution of seasonal and annual rainfall through a time.

Standard Anomaly Index (SAI).
Te SAI was used to estimate the irregularities of rainfall variations in a certain region.It helps to identify the drought period by determining the dry and wet years of the recording periods [35][36][37][38][39]. Te value of SAI is calculated by where P i is the annual or seasonal rainfall, μ is the mean annual or seasonal rainfall, and σ is the standard deviation of annual or seasonal rainfall.
According to [6,40], the SAI is classifed as extremely wet with an SAI value more than or equal to 2 and extremely dry with an SAI value less than or equal to −2, and other severity classes are described in Table 2.

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Coefcient of Variation (CV).
Te CV was used to evaluate the seasonal and annual rainfall dynamics for the observation period [8,38,41].According to Hare [3], the extent of rainfall dynamics is classifed as high (CV > 30), moderate (20 < CV < 30), and low (CV < 20).Hence, the higher the value of CV, the higher the dynamics of rainfall in the study area and the reverse is also true.Te value of CV can be determined by the following equation: where CV is the coefcient of variation, σ is the standard deviation of seasonal or annual rainfall, and μ is the mean of seasonal or annual rainfall.

Trend Analysis.
Te trend is a signifcant change of climatic data over time which is detectable by parametric and nonparametric procedures while trend analysis of a time series consists of the magnitude of the trend and its statistical signifcance [13,43].In this study, statistical signifcance  trend analysis was done by using the Man-Kendall test while the magnitude of the trend was determined by nonparametric Sen's estimator method in modifed forms (modifedmk).Te RStudio program is the most time-saving media to perform trend analysis [44][45][46].So, RStudio was selected for this particular study.

Mann-Kendall's (MK)
Test.Te Mann-Kendall's (MK) test is a statistical nonparametric test widely used for trend analysis in hydrometeorological time series data [47][48][49][50].It has been extensively applied with environmental time series after it was suggested by Mann [51].Tere are two advantages to using this test.First, it is a nonparametric test and does not require the data to be normally distributed.Second, the test has low sensitivity to abrupt breaks due to inhomogeneous time series.According to this test, the null hypothesis Ho assumes that there is no trend (the data are independent and randomly ordered).Tis is tested against the alternative hypothesis H 1 , which assumes that there is a trend.Te MK statistic is computed as follows: where x j and x i are annual or seasonal values in years j and i, respectively, n is the number of data points, and sgn(x j − x i ) is calculated as follows: A positive or negative value of S indicates an upward (increasing) or downward (decreasing) trend, respectively.If a number of data values are 10 or more, the S-statistics approximately behave as normally distributed and the test is performed with normal distribution with the variance as follows:  where n is the number of tied (zero diference between compared values) groups and t i is the number of data points in the ith tied group.Te standard normal distribution (z-statistics) is computed using the following equation: Statistically, the signifcance of the trend is assessed using the Z value.A positive value of Z shows an upwards (increasing) trend while a negative value indicates a downward (decreasing) trend.

Sen's Slope Estimator Test.
Sen's slope estimator test is a simple nonparametric procedure to estimate the true slope (magnitude of change per unit of time) if the linear trend has existed in a time series data which is developed by Sen [52].Te linear trend of the time series is expressed as follows: In the abovementioned equation, Q is the slope of the data while B is a constant value.To determine the slope of the data, the following equation can be used.
where x i and x j indicate the values of the data during the year i and j, where j > i. Suppose we have n values of x j in the time series, then N � n(n − 1)/2.Te median of N values of Q (i,j) is known as Sen's slope.
Based on the normal distribution and using the nonparametric procedure, we can achieve a two-sided confdence interval about the slope of 100(1 − α) %.An increasing or upward trend is obtained if the value of Q (i,j) is positive, while the trend will be decreasing or downward if the value of is Q (i,j) negative.

Temporal Variability Analysis Results
. Te annual areal rainfall in the Muger subwatershed for 40 years recorded data range from 890 mm to 1716 mm, while rainfall of the main rainy season, summer (Kiremt) ranges from 564 mm to 1257 mm, and for the shortest rainy season, spring (Belg) ranges from 87 mm to 485 mm.Te summer (Kiremt) season contributes about 74.5% of annual rainfall and the spring (Belg) season shears around 17.5% of the annual rainfall of the study area.Figure 3 depicts the monthly rainfall distribution of the Muger subwatershed with peaks in July and August.Te crop production in Ethiopia including the Muger subwatershed depends on these two rainy seasons.Terefore, a small fuctuation in the rainfall amount, intensity, duration, onset days, and cessation days signifcantly afects the agricultural activities of farmers [12,24,28].
Te seasonal and annual areal rainfall variation pattern of the study area in the considered time range (1980-2019) was detected by the coefcient of variation (CV).As a result, the CV value of annual rainfall is 13.43% which means the variation is low.Te highly dynamic rainfall is recorded in winter (Bega) and spring (Belg) seasons with the CV value of 50.5% and 36%, respectively.Te main valuable rainy season summer (Kiremt) in the study area shows low variability with a CV value of 13.7%.Te CV of this study agreed with previous study conducted by Mohamed et al. [53] in the Blue Nile basin revealed that the CV is high in Kiremt rainfall which implies more interannual variability of Bega rainfall than Kiremt (coefcient of variation (CV)): Bega > Belg > Kiremt season.
Te standardized anomaly index (SAI) result (Figure 4) depicts that 15% of the study period was relatively dry, another 15% was wet, and 70% was in the normal condition by considering the annual areal rainfall.As the result of SAI for annual rainfall, 1983 was an extremely dry year with a value of −2.42.Similarly, Upper Blue Nile faced extreme severe drought in the year 1980-2002 [54].Furthermore, the annual and seasonal intensity and frequency of rainfall in the study area was represented in Figure 4.
Te results of the precipitation concentration index (PCI) depict that around 17.5% of annual rainfall was strongly in irregular distribution, 57.5% of annual areal rainfall was irregularly distributed, and 25% of the considered year was moderately distributed.Mohamed et al. [53] reported that 89.9% of rainfall was irregular to strongly irregular distribution in Upper Blue Nile basin.On the other hand, the seasonal (winter, spring, and summer) rainfall distribution of the study area shows strong irregularity distribution throughout the considered years.Advances in Meteorology 3.2.Trend Analysis Results.Te trend analysis was performed in RStudio using a modifed version of Mann-Kendall and Spearman's Rho trend test with a biascorrected prewhitening technique.Hamed [55] proposed a prewhitening technique in which the slope and lag-1 serial correlation coefcient are simultaneously estimated.Te lag-1 serial correlation coefcient is then corrected for bias before prewhitening.
As the result of MK trend analysis, the areal rainfall of the Muger subwatershed was decreased in the annual and summer (Kiremt) while increasing in winter (Bega) and spring (Belg) seasons with the slope presented in Table 3. Te decreasing pattern of summer rainfall will afect agricultural practice since it is the most valuable seasonal rainfall in the Muger watershed.Most studies conducted in the Upper Blue Nile basin reported that the annual rainfall was decreasing   Advances in Meteorology trends [53,54,[56][57][58].According to the p value, the trend observed in the study area is insignifcant.
Also, the trend graph as shown in Figure 5 support the results of the modifed Mann-Kendall test.

Conclusion
Analyzing the variability and trend of rainfall time series is necessary to provide a better understanding of rainfall patterns in a specifc area.Tis study aimed to investigate temporal variability and trend in the seasonal and annual areal rainfall series recorded in the Muger subwatershed in the last four decades .Te temporal variability of the areal rainfall in the study area was analyzed by a coefcient of variation (CV), standard anomaly index (SAI), and precipitation concentration index (PCI).Te trend analysis was performed using modifed Man-Kendall (modifedmk) in the RStudio to detect the possible trends in the annual and seasonal areal rainfall.
Te results of temporal dynamics analysis indicated that the areal rainfall is variable in pattern, frequency, and distribution.Similarly, modifedmk tests in RStudio indicated that the areal rainfall of the Muger subwatershed showed a decreasing trend in the annual and summer (Kiremt) while increasing trend in winter (Bega) and spring (Belg) seasons.Terefore, the results of this study indicated that the most important rainfall season (Kiremt) is decreasing this may afect the agricultural productivity of the society.Advances in Meteorology

Figure 5 :
Figure 5: Seasonal and annual trend of areal rainfall for the period of 1980-2019.

Table 1 :
Status of meteorology stations.

Table 3 :
Statistical values of the modifedmk test.