Flow Indices Variability in Humid Subtropical of Upper Awash River Basin, Ethiopia


 Investigating the hydrological extremes indices at high resolutions describing the whole stream spectrum is essential for the comprehensive assessment of watershed hydrology. The study focuses on a wide-ranging assessment of river discharge in annual mean, peak, and high and low percentiles flow at the Upper Awash River basin, Ethiopia. Statistical tests such as coefficient of variation, flood variability to characterize the flow regime and Tukey’s test to detect decadal variability. Modified Mann-Kendall test, Sen’s slope estimator, innovative trend analysis and Pettitt’s test were applied to see trends, and change points in time series, respectively. Results showed that the basin was characterized by moderate to high variability. Spatially, main tributaries showed a higher variability, almost in all-time step and characterized by higher flood variability. The large discharge receiving rivers resulted in a moderate to high and lower discharge variability. Test statistics resulted in a positive increasing trend dominating most time scales at a 5% significant level and higher magnitude of slope trend in peak flow. A negative trends were also exhibited. Hombole main outlet site experienced decreasing trend in high percentile flow. In comparison, complete trend direction agreements were observed (except in few series). Flow indices showed an upward shift and downward shift mainly in the year 2000s and the significant decadal variation resulted in comparable with change points. The study provides an understanding of water resources variability, which will be necessary to apply operational water resources strategies and management to restrain the potential impacts of variability nature of the streamflow.


Introduction 29
Water resource management is a severe issue for sustaining the environment due to its variability. It is generally 30 understood that the chain reaction of climate variability and land use land cover change impacted the 31 hydrological cycle components (Legesse et al. 2003(Legesse et al. , 2010Bao et al. 2019;Liu et al. 2020). In the first instance 32 mainly, extreme hydrological events such as floods and droughts are of consequences (IPCC 2014). Climate 33 change impact on streamflow is extensively studied. In particular, precipitation and temperature change are 34 sensitive to change in streamflow characteristics (Hailemariam 1999 Although, at main river outlet, for instance, Hombole station conflicting trend results were reflected on the 76 annual scale. These studies focused on detecting the homogeneity tests and trends in hydroclimatic variables 77 using commonly MK test and Sen's slope estimator at courser time scales. Long-term hydroclimatic evaluation 78 alone cannot be satisfactory in understanding the pattern characteristics of temporal variations and it is important 79 to examine at different time scales. It has the advantage of defining the entire range of flows observed each year. 80 Moreover, water managers are interested in flood and drought assessment in a basin like Awash River basin 81 where surface flow availability depends on precipitation for rainfed and agricultural irrigation as the backbone 82 of the economy and food security. In this case, though there have been studies on long-term streamflow 83 variability in the river basin under investigation, and it could not describe the high-resolution variations. 84 Investigating the hydrological extremes indices at high resolutions describing the whole stream spectrum is 85 essential for the comprehensive assessment of watershed hydrology. 86 The annual mean, annual peak flow, and percentiles flow of 99 th , 95 th , 90 th defined as the high flow and low 155 flow as 10 th ,5 th , and 1 st were extracted for analysis from daily data series. Considering large sets of hydrological 156 variables enables us to explore the broader impacts of the climate and anthropogenic on watershed hydrology. 157

Statistical Analysis 158
In order to provide the existence of healthy hydrological characteristics over the historical period, coefficient of 159 variation and discharge variability index were used in this study to explore further variability in hydrological 160 indices. The statistics of coefficient variation (CV) is the ratio of standard deviation to mean. This study 161 employed coefficient of variance to summarize streamflow variation degree to mean streamflow record periods 162 of annual mean, annual peak and percentile flows and determine the significant level of variation in the data 163 structures. CV has been applied in the long term hydroclimatic variability studies (Chen et  In addition, Tukey's HSD (honestly significant difference) multiple comparison test was used to evaluate 171 the pattern of difference between means. Before Tukey's HSD test, if the analysis of variance among the groups 172 of means is significant, it means at least one group differs from the other groups, and detail can be referred from 173 Williams and Abdi (2010). Tukey's test at a decadal resolution of the annual mean flow, peak flow, 95th and 174 10th percentile flows was applied to test the mean variability. The time interval was selected from 1970-1979, 175 1980-1989, 1990-1999, and 2000-2009. All pairwise differences were evaluated using the same sample size 176 used for the most significant difference. The null hypothesis assumed that there was no significant difference 177 between means and the alternative hypothesis was assumed that a significant difference exists in means at a 5% 178 significance level. The Tukey's HSD appraoch has been applied to test the hydrological variation in decedal 179 resolution in Lake Tana Basin, Ethiopia (Tigabu et al. 2020). 180

Mann-Kendall Trend Test (MK) 182
In the current study, a robust non-parametric MK trend test (Mann 1945a;Kendall 1975) The data series variance ( ) was estimated by: 190 Where, is the length of observations, is the number of pairs observation in data series, is the number of 191 pairs observations in series at the time .
The value determines the existence of increasing, decreasing, and no trend in time series. When value 195 is greater than zero, it indicates the increasing trend, and a negative value suggests decreasing trend. The critical 196 value at a two-tailed 1%, 5%, 10% significant level is ±2.576, ±1.96 and ±1.645. In this study, 5% significant 197 level was used to detect the trend and a significant increase or decrease is accepted if the > ± 1.96 (Diop et 198 al. 2017) 199

Modified Mann-Kendall Trend Test (MMK) 200
The existence of serial correlation leads to the rejection of the null hypothesis (no trend) and accepts the 201 Where k r is the lag-k serial correlation of the observed serial and N is the total length of the data series.

211
Variance correction approach has been used to correct the serial correlated hydrological series data by many 212 latest studies and detected the trend to corrected variance (Wang et al. 2015;Azam et al. 2018). The test was 213 applied for annual mean, peak and high and low percentile flows at lag-1 to detect trends in the flow indices. 214

Sen's Slope Estimator (SSE) 215
If a trend exists, the magnitude of linear trend slope in time series is estimated using a non-parametric approach 216 (Theil, 1950 andSen, 1968). Monotonic trend slope was calculated using: 217 and are the data observation corresponding to time and . The median of = ( − 1)/2 for is 218 Sen's estimator of the slope where is the number of periods. The is tested against the two-sided test at 5% 219 significant level and the actual slope is estimated by a non-parametric test. The sign of the obtains the 220 increasing if is positive and decreasing if is negative. 221

Innovative Trend Analysis (ITA) 222
The ITA was first developed by (Şen 2012). The data time series is divided into two equal sub-series and ordered 223 in ascending. The first half time-series sets are placed in the x-axis, and the second half time data sets are also 224 placed in the y-axis in the Cartesian coordinate system. If the two sub-series are alike, the data points in the plot 225 Where ̅ and ̅ are the arithmetic average of the first and second half time series, respectively, and is 231 the data set length. The stochastic property of S is a function of the arithmetic mean of the first half and second 232 half time series. As ̅ and ̅ are also stochastic variables, the first-moment order (expectations) of the slope 233 trend can be obtained by taking the expectation of both sides: 234 In case of no trend detection, the centroid point fall on the 1:1 line (45 0 ), indicating that ( ̅ ) = ( ̅ ) and 236 hence, ( ) = 0. Then again, the variance of the slope can be computed as 2 = ( 2 ) − 2 ( ), which is 237 equal to the second-order moment of the slope variable. Since ( ̅ 2 ) = ( ̅ 2 ), then the variance of slope 238 equation can be expressed as; 239 The correlation coefficient of the two mean values in the stochastic process is expressed: 241 Substituting the correlation coefficient of the two mean numerator into Eq. (11) and considering ̅ = ̅ = 243 /√ gives the variance of the slope as follow: 244 Where, ̅ ̅ is the correlation coefficient of the two mean values in the stochastic process, finally the standard 246 deviation of the slope is given: 247 Therefore, the statistical significance of the innovative trend slope test can be achieved through a normal 249 (Gaussian) PDF with zero mean and standard deviation equal to . If at α percent significance level, the 250 confidence limits of a standard normal PDF with zero mean and the standard deviation is Scri, then the confidence 251 limits (CL) of the trend slope is obtained as: 252 Where denotes significance level and is the standard deviation of the slope. The null hypothesis, H0, 253 infers that there is not a significant trend if the calculated slope value, , remains less than a critical value, . 254 Otherwise, an alternative hypothesis, Ha, is accepted when > . In this study, 5% significance level was 255 used for the ITA approach to mean annual, peak, high and low percentile flows. 256

Change-point Analysis 257
A non-parametric Pettitt's test (Pettitt 1979) was used to detect the abrupt change in the middle of the data series. 258 This test was chosen because it is free distribution testing, adaptation of the rank-based Mann-Whitney test and 259 has the advantage of sensitivity to identify the exact time of step change is anonymous. The method was most 260 widely used in hydrological and climatological data (Kundzewicz and  , ,1 p, of the sample n length and its associated K statistics, 266 In this study, the 5 % significance level was considered. The null hypothesis of change not exist is rejected 268 if the p values is less the specified significance level (α = 0.05) and accept the alternative hypothesis, change 269 exist in the data series. The constancy statistical properties (stationary) of the stream flow indices before and 270 after change point was evaluated by plotting probability of exceedence against descending order of stream flow 271 of two group (before and after) using Weibull plotting position (Rao and Hamed 2000), / + 1, where i is rank 272 in ascending order and n is the number of observations. Probability of exceedence of 10%, 50% and 90% was 273 chosen to compare the discharge both before and after change point. 274 values during Kiremt (Fig. 2b). In addition, there was no significant dissimilarity in mean in all stations between 294

Results and Discussion
October and June. Thus, the observed discharge value corresponds with the highest and tiny rainfall season. 295 Over all spatial patterns of mean annual and mean monthly discharges are similar. 296 The streamflow variability in mean annual flow, peak flow and percentiles flow was defined by the 299 coefficient of variation (CV) statistics and is given in Table 2 and Table 3. Almost 66.6% of the station have 300 shown high (> 0.3) variability in mean annual and peak flow series, respectively. Remarkably, as far flood is 301 the concerned in the tributaries, the peak flow time series in tributaries were found to have high variability 302 dominates in the region followed by moderate. Stations at main river also depicted high variability. It can be 303 seen that the CV value of the two river is almost similar in the mean annual and high percentile flow series,  The Flood regime characteristics, the ratio of annual maximum streamflow to mean annual flow 319 (Qmax/Qmean), was calculated for the individual station and shown in Fig. 3 The river discharge changes were evaluated at decadal resolution considering annual mean, peak, 95 th and 10th 331 percentile flows series ) are representative data sets. Moreover, the data sets were checked against 332 variance of the group mean difference is significant. Using Tukey's test, decadal mean flow variability exhibited 333 that three stations of the different resolution had a significant difference in mean at α = 0.05. The mean annual 334 discharge of Melka Kunture between the 1980s and 2000s depicted a significant increase and the mean 335 difference between the two decades was significantly different (Fig. 4a). The mean variation between the 1970s 336 and 1980s, 1970s and 1990s, 1970s and 2000s, 1980s and 1990s, and 1990s and 2000s were insignificant. In 337 95 th percentile flow, the mean significant increase from the 1980s to the 2000s was exhibited (Fig. 4c). In the 338 case of Mojo station, the decadal mean annual flow (except for the 1970s and 2000s) variation was significant 339 (Fig. 4b). The flow was significantly increased between the 1970s and 1990s and insignificantly decreased from 340 the 1990s to 2000s. The 1990s mean annual flow was highly significant compared to the 1970s (Fig. 4b). In 341 peak flow, decadal mean variation was a significant increase between the 1970s and 1990s and a significant 342 decrease 1990s and 2000s (Fig. 4d). The highly significant mean difference was shown between the 1970s and 343 1990s. The peak flow of the rest decades did not show significant variation. The 95% percentile flow for Mojo 344 indicated a significant increase from the 1970s to the 1990s and a significant decrease between the 1990s and 345 2000s (Fig. 4f). It is, therefore, apparent mean decadal variations exist between periods.   Table 4 presents the summary results of temporal trends by modified MK trend and magnitude of the trends by 368 Sen's slope in mean annual, peak, high and low percentile flow time step at 5% significance level (Zcritical = 369 1.96). The Z statistics of mean annual was evident that a mixture of positive and negative trends, indicate 370 increasing and decreasing trends. In most stations, the mean annual series showed that increasing trend but 371 statistically not significant. MMK statistics exhibited decreasing trend (Holeta and Mojo) and an increasing 372 trend (Berga,Teji, Melka Kunture and Hombole). The magnitude of decreasing and increasing trend rates using 373 the Sen's slope were also provided in Table 4. The least trend magnitude was observed in mean annual flow 374 time series. 375 result indicated that most of the stations in tributaries were characterized by increasing trends and higher trend 381 magnitude in main river section. 382 The trend of mean annual detected by ITA was presented in Table 5. The result showed that slope S of mean 383

Trends in Peak Flow 398
The temporal peak flow trends detected by MMK test and trends magnitude by SSE were presented in Table 4. 399 In peak flow time series, most of the stations exhibited increasing trends (except Holeta and Hombole); however, 400 Significant increasing trends was observed in Teji station (1.53 m 3 /s year -1 ) and Berga (0.23 m 3 /s year -1 ). The 401 decreasing rate of 1.09 m 3 /s year -1 at 95% confidence level was exhibited at the outlet of Hombole station. The 402 spatial pattern of trend magnitude at Mojo station, the increasing rate is as high as 2.086 m 3 /s year -1 , followed 403 by Melka Kunture at rate of 1.79 m 3 /s year -1 . 404 Peak flow trend test using ITA method was given in Table

Trend Change-point Analysis 481
Abrupt changes may be attributed to natural or anthropogenic changes in climatic, hydrological or landscape 482 process (Ryberg et al. 2020). In this study, the Pettitt test was carried out to investigate change point in annual 483 mean, peak and high and low flow percentile flows considering a 95% confidence level. The change test result 484 was summarized in the Table 7 -2005  2005  -1983  99th  -2005  2003  -2000  95th  --2003  -2001  90th  ----2000  10th  2004  1995  ---5th  2004  1994  ---1st  2004  1994  -2005  The hydrological series exhibited trends and change points, which are indicative of the nonstationary 507 properties of the hydrological indices. The shape of the probability of exceedence curves before and after a 508 breakpoint, and the nonstationary series of the peak flow was shown in Fig. 9. The magnitude of the peak flow 509 exceeded or equaled to the specified exceeded probability scales are obtained for comparison before and after 510 the change point. In Fig. 9, the exceedence probability curve demonstrated that the peak flow after the change 511 point was found upward. For instance, for Teji station, the flood magnitude equaled or exceeded 10%, 50%, 512 90% of the time increased by 53.75, 52.14, and 62.66 m 3 /s, respectively. The highest magnitude of change was 513 seen in Melka Kunture followed by Mojo after the change point for the specified exceedence probability. Thus, 514 the peak floods after the change point were more significant than the peak flow before the change point equaled 515 or exceeded 10%, 50% and 90%. 516 increased after 1995. In sum, this significant increment in peak flow in the tributaries, mainly upstream, 531 exacerbates the continuing flooding during the heavy rain periods (July and August). Thus, the increasing human 532 activities impact flooding and water availability in the future should be the primary concern, principally seasonal 533 peak flow and requisite land-use management intervention in the basin. 534

Comparison of modified MK trend test and ITA 535
For the 12 mean annual and peak flow series evaluated by the MMK test and ITA method at 5% significant 536 level, significant trends were observed in 2 series by MMK test and 8 series by ITA method. ITA also detected 537 all significant trends identified by MMK test. The two trend analysis approaches revealed that 2 series in annual 538 mean were inconsistent with the sign of the trend (opposite each other). It was also noted such difference by two 539 methods in hydroclimatic trend assessment (Belihu et al. 2018). It is noted that there was complete agreement 540 in directions between the trend tests, 8 increasing and 4 decreasing trends (including significant) by ITA and 8 541 increasing trends (including significant) and 4 decreasing trends by MMK test method. Also, the ITA method 542 detected significant trends in mean annual and peak flow series that the MMK test has not identified. The trends 543 statistics in the 36 high and low flow percentile series by MMK and ITA show that significant trends/directions 544 were detected in 16 series by MMK and 32 series by ITA method, including the significant trends identified by 545 MMK test. The 4 series in the high and low flow percentile showed disagreement with the trend sign. In sum, 546 the closing agreement is observed between the MMK and ITA, 20 increasing and 16 decreasing trends were 547 identified by MMK and 23 increasing and 13 decreasing trends were also seen by ITA including significant 548 trend. In these tests, significant trends in time series that are not recognized by the MMK test are successfully 549 spotted by ITA tests. ITA approached revealed more significant trends in the time series (increasing and 550 decreasing trends) and included all significant trends identified by MMK. 551 In the present study, the agreement among the signs of the trends is observed but is not entirely consistent 552 with significant trends. ITA method proved the ability to graphically show the non-monotonic trends in the same 553 time series or hidden trends compared to the MMK test, helping to examine the flow properties in groups. It is 554 rational to use ITA method to scrutinize the sub-trend in hydrological series rationally. In the case of this study, 555 it was seen that the high flow region shows a substantial increase and decrease. As far as the flood is concerned 556 in the region, the significant increase of high group in peak flow of the Melka Kunture station was observed. 557 The present study performed a very different look from classical trend analysis for high-resolution hydrological 558 data series. The classical MK and Sen's slope give overall trends directions and do not provide sub-trends 559 graphically and respective quantitative estimation. Thus, ITA delivers clear insight into the temporal variability 560 of hydrological series and is crucial to identifying the flow cluster that is increasing or decreasing for effective 561 management of extreme hydrologic events in the basin. 562 In summary, it is essential to note that discharge variability varies spatially in terms of mean annual, peak, The study of streamflow characteristics in planning and developmental activities such as hydropower, 596 irrigation, water supply projects, drought and flood, its impacts on operational and efficient functioning are 597 imperative. In hydroclimatological time series observation, the recent human activities and climate variation are 598 two major determinant factors that invalidate the stationary assumption in hydrological studies (Milly et al. 599 2008). Thus, hydrological studies, water resource planning and management to account the adjusting land cover 600 land use and climate change in the basin. Therefore, in agreement with this study, it was seen that the UARB 601 streamflow trend and change matches with previous studies in and around the region. This study examined the 602 spatial characteristics of temporal trends and change in peak, high and low flow percentiles time series in high 603 resolution. The spatiotemporal depth analysis of river discharge provides insight into better water resources and 604 flood management in the basin. Thus, the detail information of flow characteristics can be described using higher 605 resolution than the courser (e.g. seasonal flow evaluation). 606

Conclusions 607
The study aimed to investigate hydrological variability, trend and change in hydrological indices of the UARB. 608 Statistical tests such as coefficient of variation were used to explore the variability, flood variability to 609 characterize the flood regime and Tukey's test to evaluate decadal mean variation. The modified MK test, SSE 610 and recent ITA were also applied to detect trends and Pettiitt's test to identify probable change time in 611 hydrological time series in different time steps, annual mean, annual peak, and upper and lower percentile scale 612 at 5% significance level. Based on the assessment attempted, the spatial flow indices variability, trend and 613 change over the basin were concluded as follow: 614 Rivers discharge varies spatially from the lower amount in the upper to higher in the lower reach. The 615 interannual coefficient of variation of UARB was portrayed as moderate to high variability in discharge series 616 and most of them exhibited high variability. Flood regime characteristics were found higher in main tributaries 617 than the main river, implying high discharge variability in branches. The spatial pattern of the variability in 618 tributaries was exhibited as high. Tukey's multiple mean difference comparison technique was applied and few 619 stations series showed significant differences between the mean of groups. Significance increase and decrease 620 in mean difference between the mean of groups was noted and enabled to confirm the change point, for instance, 621 in the 2000s. 622 The serial correlation test identified most of the station time series were serially correlated. Based on the 623 assessment, a modified Mk test based on the variance correction techniques was utilized to reduce the effect of 624 autocorrelation. The modified MK test and ITA, and SSE revealed increasing trends were dominant, followed 625 by decreasing tends in the basin at 5% significant level in the all-time series considered in the study. Significant 626 decreases and increases were identified in low percentile flow in tributaries. The higher magnitude of increase 627 was revealed in the branch river in peak flow series at Mojo station. Notably, it was noted that there was an 628 agreement between the two trend analysis approaches in terms of positive and negative statistics values. In some 629 series, the opposite sign of trends was identified. The two trend analysis methods were able to signify the 630 temporal hydrological variability over the basin, but the ITA method can detect the sub-trends than the modified 631 MK test and does not require a serial correlation test in time series. Based on these assessments, the discharge 632 Higher resolutions of diverse data scales are essential to remark the difference in the spatiotemporal 641 variability of river discharge and able to detect in depth variation. The flow variability reflects the causes and 642 probability of flood and drought in the tributaries. Integrated water resources management is necessitated to 643 overcome the water resources management aspects and flow control severely limits variability in the tributary. 644 The study provides an understanding of water resources variability in depth, which will be necessary to apply 645 operational water resources strategies and management to restrain the potential impacts. 646 647 648 Acknowledgments 649 The authors acknowledge the Ethiopian ministry of water resources, irrigation and electricity for providing 650 hydrological data. 651