Trend Analysis of Climate variables, Stream flow and their Linkage at Modjo River Watershed, Central Ethiopia

Background: Trend and variability analysis of precipitation and stream flow series provides valuable information to understand hydrological changes associated with climate variability. In this study, annual and seasonal trends of precipitation and stream flow series and their relationship was investigated over the Modjo river watershed. The Mann-Kendall test and Sen’s slope estimator were used for trend analysis and evaluation of its magnitude respectively, with an approach that corrects the serial correlation. The Pearson correlation analysis was also applied to evaluate the relationships between river flow and precipitation series. Results: the mean and maximum stream flow series showed downward trends at the annual and kiremt time series, whereas no significant trend was observed for the minimum flow over the Modjo watershed. The study indicated that the mean annual and kiremt (monsoon) stream flow decreased significantly at a rate of 8.262 and 6.528 m 3 s -1 per year respectively. In contrary to the river flow, there is no positive or negative trend in the annual and seasonal precipitation series although the tendency was towards increasing trends. It was evidenced that the annual, and kiremt season river flow series was affected abruptly since 2000, however for the same analysis period there was no evidence of changes in precipitation events, which is also not related significantly with the variability of river flow during the analysis period. Conclusions: the river flow decreased dramatically in the Modjo watershed during the analysis period (1981-2015), however it was not primarily associated significantly with climate variability (precipitation & temperature). The result suggests the need of considering the unplanned water extraction and the poor land use management practices to sustain and restore river flow trend observed in the watershed. will the of the Pearson’s correlation test was used to evaluate the correlation between stream flow and climatic variables. The results indicated that stream flow is more sensitive to changes in precipitation than potential evapotranspiration at the respective catchments. Furthermore, the study conducted by Akter et al. (2019) investigated the relation between stream flow and precipitation, and their finding revealed that strong relationships between river discharge and precipitation at the annual and seasonal over the study area. It is clear from the literatures reviewed above that the hydro and climatic parameters can be correlated using the Pearson’s coefficient, and indicated that precipitation and stream flow are major hydrologic variables followed by temperature, which attracted the attention of researchers from different of for applying different time series analysis approaches.


Introduction
Water resources projects are planned, designed and operated based on the historical pattern of water quality, availability and demand with the assumption of constant climatic behavior. It is therefore important to investigate present and probable future climatic change patterns and their impacts on water resources so that appropriate adaptation strategies may be implemented by decision makers.
Climate variability affects water flow directly. Specially, the variability of precipitation type, frequency, intensity, amount and duration, and also its trends (increasing or decreasing) can have significant impacts on water resource management, utilization, quantity and quality in general. That means, the sustainability of water resources (i.e., ground and surface waters) can be directly affected by the precipitation characteristics of the region. This in turn may have the potential to affect land productivity, agricultural activity, food security and ecosystems. Abghari et al. (2013) indicated that climate change will lead to an intensification of the global hydrological cycle and can have major impacts on surface and groundwater resources. Over the last fifty years, it is evidenced that the greenhouse gases has affected the global water cycle by changes to the intensity of heavy precipitation, increased frequencies, increasing annual runoff in some highland regions, and appearance of sudden droughts (Dai et al. 2004;Milly et al. 2005).
Spatial and temporal trend and variability analysis in hydrologic and climatic data obtained from instrumental records are valuable in water resource investigations. Changes in river flow regime are one of the most significant potential consequences of climate change (Khaliq et al. 2009). It is understood that if precipitation and temperature are changed, stream flow regimes can be changed significantly and as a result of this, it leads to the appearance of floods and droughts (Dai, 2013). In the recent times, time series analysis has emerged as a powerful tool for the efficient planning and sustainable management of the scarce water resources. Time series analysis on hydrological and climatological data have been carried out in different parts of the world in the last century, for example, to analyze historic rainfall data trends (Brunetti et al. 2000;De Luís et al. 2000;Astel et al. 2004;Kumar et al. 2010;Bekele et al. 2017;Mahtsente et al. 2019), for stream flow data trends Fanta et al. 2001;Adeloye and Montaseri, 2002;Alemaw and Chaoka, 2002;Chen and Rao, 2002;Cunderlik and Burn, 2002;Kahya and Kalayci, 2004;Cherinet et al. 2019), and climate change impact detection (Yu et al. 2002).
The relationship between precipitation variability and river flow changes is an important watershed phenomena and that is why great concerns have been paid in most studies in the recent times. The studies by Jones et al. (2009) and Teng et al. (2012) on their respective catchments for example, indicated that changing precipitation patterns and intensity, together with changing temperatures, will hugely modify the stream flow of a basin. On the other hand, in the study conducted by Zhao et al. (2010) over the Poyang lake basin of China and Uddin et al. (2017) in the Kushiyara river basin of Bangladesh the Pearson's correlation test was used to evaluate the correlation between stream flow and climatic variables. The results indicated that stream flow is more sensitive to changes in precipitation than potential evapotranspiration at the respective catchments. Furthermore, the study conducted by Akter et al. (2019) investigated the relation between stream flow and precipitation, and their finding revealed that strong relationships between river discharge and precipitation at the annual and seasonal over the study area. It is clear from the literatures reviewed above that the hydro and climatic parameters can be correlated using the Pearson's coefficient, and indicated that precipitation and stream flow are major hydrologic variables followed by temperature, which attracted the attention of researchers from different parts of the world for applying different time series analysis approaches.
Almost all agricultural activities in Ethiopia are done by waiting the seasonal rainfall. For this reason, trend and variability analysis in precipitation and stream flow is important to understand the past and for sustainable planning and development of water resources of the future. Furthermore, the choice of crops, grown times, cropping pattern and the agricultural productivity in catchments are also hugely determined by hydrologic and climatic conditions of that area and its neighbors. Even though several studies have been conducted on trend and variability in precipitation and river discharge and their relationships all over the world, a few studies have been conducted in Ethiopia at spatial and temporal time scales (for example, Edossa et al. 2010;Tesemma et al. 2013;Wagesho et al. 2013;Mengistu et al. 2014;Bekele et al. 2017;Mahtsente et al. 2019) are some of the studies conducted at large basin such as the upper Blue Nile and Awash river basins. But no adequate attention has been given to trends and variability of rainfall and river flow, and their relationships at the watershed scales.
Modjo watershed is one of the intensively cultivated watersheds in Ethiopia. As in the other parts of the country, the agricultural activity of this watershed is entirely dependent on rainfall and only small amount of irrigation has been practiced at individual levels. For an area that is entirely relay on natural rainfall, understanding of the hydro-climatic condition is highly valuable; first to known their trends and variability through time and secondly the impact of one would have on the other parameters. The Modjo river shows a decreasing trend but there is no study conducted before to understand the cause of this trend. Therefore, this is the first attempt on hydrology and climate trend analysis in the watershed. With this consideration in mind and to add some valuable points onto the existing literatures, therefore, a thorough investigation of hydro-climatic data was conducted to analyze temporal trends of precipitation and stream flow records and their relationship for the period 1981-2015. The specific focuses of this study were; (1) to examine trends of hydro-climate variables at annual and seasonal time series, (2) to detect the abrupt change point in precipitation and stream flow series, and (3) to analyze the relation between stream flow and precipitation to understand the impacts of climatic changes on river flow. The findings of this study are expected to assist water resource managers and policy makers for better water resource planning decisions in the study watershed.

Description of the study area
The Modjo river watershed is the sub basin of the Awash river basin, of Ethiopia. It is located in the central part of Ethiopia between latitude of 8°35′00″N to 9°05′11″N and longitude of 38°54′35″E to 39°15′30″E. The study watershed is drained to Awash river by the Modjo river ( Fig. 1). This watershed is characterized by a rugged and undulating topography with higher elevation at upstream of the watershed, and its elevation varies between 1568 m and 3084 m above sea level, which shows that the elevation difference between the highest and lowest point (i.e. outlet) of the watershed is more than 1500 m, indicating part of the Ethiopian highlands.
On the basis of the 1981-2015 recorded data, the watershed receives mean annual rainfall between 950 mm and 1100 mm. The annual mean minimum temperature varies between 11-12 o C and mean maximum temperature varies between 26-30 o C, whereas the annual average temperature of the watershed is estimated and varies between 19 o C and 21 o C. The Modjo river and its tributaries have been used as the main source of water supply to major towns such as Bishoftu, Modjo, Edejere, Chefe donsa, Koka town and other rural communities within Oromia regional state. Furthermore, there have been a number of water wells (i.e. hand dug and tube-wells) bored near the river-bed to exploit ground water for domestic and other different types of industries (for example, Paint industry, Textiles, Tanneries, steel industries, Oil factors, etc.), which are currently existing in the watershed. In general, the river becomes of water-stressed because of high competing demands and improper land use and management practices. However, the impact of these demands, relative to the natural flow regime, is of high and significant. In addition, from socio-economic, hydrological and geomorphological characteristics points of view, the catchment is highly susceptible for surface erosion & sediment deposition problems; reduction in surface water flow, intensively cultivated; highly grazed and relatively densely populated area.

Data types and sources
For this study, precipitation (4 stations), stream flow and runoff data were used to evaluate trends in climate and hydrology and relationships between them. The daily stream flow and runoff record data

Statistical Methods
In this study, all the trend tests are conducted through the 'Monte-Carlo experiments' featuring over 10,000 runs (unless stated otherwise) using precipitation and river flow time series data of record length, N = 35. Four types of tests were used: Mann-Kendall (a trend test); Sen's slope estimator (a trend magnitude test); Pettit (a change-point test) and Pearson's coefficient (correlation test), as described in sections below:

The Mann-Kendall (MK) test
The MK test series (Mann, 1945;Kendall 1975;Zhang et al. 2006) is a powerful tool in exploring trends of hydro-climatic time series. The test is robust and very useful in many hydrological studies for detecting trends (Hirsch and Slack 1984), and also recommended by the World Meteorological Organization (WHO) to assess the significance of monotonic trends in stream flow series (Mitchell et al. 1966). The null hypothesis H 0 states that the de-seasonalized data (x 1 ,. .. ,x n ) are a sample of 'n' independent and identically distributed random variables (Yu et al. 1993). The alternative hypothesis H a of a two sided test is that the distribution of x k and x j are not identical for all k, j ≤ n with k = j (Kahya and Kalayci 2004). Equations (1) and (2) are used to calculate the test statistic (S): Where: x j and x k are annual values in the year j and k, j > k respectively. The trend test is applied to x k data values (ranked from k = 1, 2,. . ., n − 1) and x j (ranked from j = i + 1, 2,. . ., n). For the sample size, n lower than 10, then the Mann-Kendall test statistic, S is correlated directly to the theoretical distribution. However, for a sample size larger than n (n ≥ 10), with the mean E(S) = 0 and standard deviation σ s is given by Where: n is the number of observations; x j and x k are the data values in two consecutive periods, r is the number of tied groups, and t i is the number of ties (i.e. equal values, of extent i  . To investigate serial correlation, the data was correlated through trend free pre-whitening (TFPW) approach to remove the correlation for the MK test.

Pettit change point detection test
The Pettit's test is recognized as a useful method for change point detection (Love et al. 2010;Gao et al. 2011;Tekleab et al. 2013). According to this test, for a sequence of random variables X 1 , X 2 , …, X T there is a change point at τ (X t ) for t = 1,2,…, τ have a common distribution function F 1 (x) and X t for t = τ + 1, … T have a common distribution function F 2 (x), where F 1 (x) ≠ F 2 (x) (Pettit 1979). The formula shown in Eq. (5) was used to estimate the non-parametric test statistic: In which: K is the location of the final change point and T is the date of change provided that the statistic is significant. The significance probability associated with the rejection of H 0 , within 1% for p < 0.5 is approximated by: Equation (6), however does not give any confidence that T is the date of a shift, as it merely reports the greatest likelihood of a change in the median. In general, the test was evaluated against a userdefined significance level (α = 5% in this case) and when p is smaller than the specified significance level, the null hypothesis (that states no significant difference between the mean values of the two sub-series) is rejected.
In addition, statistical features of the segments divided by change points are detected by the mean and coefficient of variation (CV). In this case, the mean is the arithmetic average of random variables and calculated using: A dimensionless measure of dispersion is the coefficient of variation, defined as the standard deviation divided by the mean. The coefficient of variation (CV) is estimated using Eq. (8):

Sen's trend slope estimator
The change per unit (true slope) is estimated by using the Sen's method, which is a simple and nonparametric technique developed by Sen (1968). This method is selected as it is more robust to outliers compared to the parametric tests such as linear regression (Hirsch et al. 1982). For two data points of x j and x k at j and k (where, j > k), the slope, β was estimated using Eq. (9): Considering t as the length of analysis period (in years), the following equation gives the trend magnitude in percent change over the analysis period (Lehmann et al. 2005).

Relations between climatic and river flow
The correlation of parameters is a useful statistical analysis approach that can be used to construct comprehensive relationships between parameters in the baseline period (Hastenrath, 1990;Chen et al. 2007;Burn 2008;Xu Jianhua et al. 2008;Zhao et al. 2009 andUddin et al. 2017). In this study, the relation between trends in precipitation and stream flow was examined using the Pearson correlation coefficient at 5% significance level. For this purpose, Eq. (11) was used to estimate the correlation between stream flow (X i ) and precipitation (Y i ) variables: Where: N is the series length, and are departures from the mean values of and respectively, "r" is Pearson's coefficient of correlation. Then, the Student's t-distribution with degrees of freedom n -2 was used to assess the significance of the Pearson's product moment correlation coefficient (Hirsch et al. 1993). The estimated correlations were tested for statistical validity at the 5% level of significance. The r values − 1 and + 1 correspond to perfectly negative and perfectly positive linear correlation, respectively, while r = 0 indicates there is no correlation between parameters (i.e. stream flow &precipitation in our case).
To indicate the proportion of the variance in the dependent variable (i.e., the one predictable from the independent variable), we used the coefficient of determination (i.e., the square term of coefficient of correlation, r), which is usually used by different research studies (for example, Numanbakth et al.

Change point detection in Precipitation and Stream flow
The Modjo watershed experienced significant change points for stream flow but not for precipitation    respectively. Since 2000, the decline in runoff during the wet season has been severe at the 5% significant level.

Annual trends in precipitation
The monthly precipitation amount is highest in August and lowest in December at all the stations. The annual mean precipitation of the study watershed is 1006.6mm, with coefficient of variability (CV) of 15.24% during the analysis period . The highest and the lowest annual precipitation

Seasonal trends in Precipitation
Trend analysis was also evaluated for the seasonal precipitation data in the Modjo watershed for the same analysis period. The MK test statistics of the seasonal precipitation is shown in table 5. During the study period, the seasonal precipitation showed non-significant trends in most of the stations.
Precipitation in the monsoon (kiremt) and pre monsoon (belg) months showed non-significant trend in most of the stations except at Edjere. At Edjere station statistically significant increasing trend was detected during the main rainy months (June to September), with a trend slope of 0.126mm/year during the analysis period. In general, the monsoon months precipitation was insignificantly decreasing at Debre zeit and Edjere stations, whereas at Chefe donsa and Modjo stations statistical non-significant increasing trend were exhibited at 5% significant level ( Table 5). During the 1981-2015 period, the small rainy or belg months (March to May) precipitation generally indicates nonsignificant decreasing trend (p>0.05) in all the stations we considered ( Table 5). Precipitation data from the four stations were used to evaluate trends in the Modjo river watershed during the period 1981-2015. The analysis of annual and seasonal trends generally indicated that no significant trends were detected in the annual and seasonal precipitations over the watershed. This may be due to the sample size we considered. Hence, to get clear trends in the recorded data, it should be tried by using better sample size.
Previous studies have found almost similar results with this study for the annual rainfall totals in central highlands of Ethiopia (Seleshi and Zanke 2004), in which our study area is located. This study is partially in a good agreement with the study conducted by Mahtsente et al. (2019) who did not detect any statistical significant trends in annual and belg season rainfall series at Modjo and debre zeit stations.

Annual trends in river flow
The annual trends were evaluated for the three distinct hydrologic variables: minimum flow,  Analysis of the mean stream flow recorded data at Modjo river  indicated the mean stream flow was peaks during the 1996's (1296.24 m 3 s -1 ) than any decade since its monitoring time (1968's). The magnitude of stream flow events that occurred during the 1996's was atypical of historical peaks of the river. However, the MK trend analysis revealed that a highly significant decreasing trend was detected in the mean stream flow records with an estimated trend slope about 8.262m 3 s -1 and a significance of 0.00 during the analysis period (Fig. 4). In general, the downward trends in the annual mean and maximum flows may be explained by the impacts of uncontrolled water use/extraction for different purposes, and the availability of lakes and wetlands in the watershed.

Seasonal trends in river flow
Three distinct seasons have been considered for trend analysis, they are bega or base flow (October -February), kiremt or high flow (June -September) and belg (March -May). During bega (dry) period, stream flow is fairly uniform and follows at constant rate. The flow during the kiremt period follows the rainfall period and generally begins about early in June and extends until September. Usually, river flow during the Ethiopian summer period is highly variable. During this period, the stream flow decreases fairly quickly after peaking in August. In the belg season flow begins early in March and extends until about May. Early in this period, stream flow increases substantially from base-flow conditions (Fig. 5).
In this study, no statistically significant trends have been detected in the minimum flow (base flow) series during the kiremt and belg seasons over the watershed at 5 % significant level. However, this flow showed a significant increasing trend during the dry period with a rate of 0.025m 3 s -1 per annum (Table 6).
Maximum flow is usually associated with floods in the central highlands of Ethiopia as it induced by kiremt season precipitation. The maximum stream flow series during kiremt season (June -September) showed highly significant decreasing trend, with a percentage decline of 87.04% over the study period (Table 6). However, the belg (March to May) and bega (October -February) seasons of the maximum flow data experienced statistically non-significant decreasing & increasing trends, in that order at 5% significant level. In summary, there was no uniformity in trends between precipitation and river flow series in the study area and in fact, opposite trend directions (nonsignificant for precipitation and significantly decreasing for river flow) were observed over the analysis period.
The mean flow series during kiremt season (monsoon) showed a significant decreasing trend at a rate of 8.262 m 3 s -1 per year (Table 6). Whereas, during the dry (bega) season the stream flow showed statistical significant increasing trend with a rate of 0.048 m 3 s -1 (7.55%). This is very important for the area as the local communities are mostly relay on surface waters sources (i.e. river and lakes) and its small tributaries for their various uses. On the contrary, the small rainy (belg) season flow record experienced statistically non-significant downward trend at a decline rate of 0.102m 3 s -1 (19%) per year at 5% significant level.
For the same analysis period, precipitation and river flow showed an inverse trend both for the annual and seasonal time series. The river flow, showing a drying tendency since it showed a statistically significant declining trend (particularly in the annual and wet seasons) during the study period (Fig. 5   & 6). From the statistical analysis, a downward trend in mean and maximum stream flow series was obtained without any significant changes in precipitation in the study area. Therefore, human factors (such as land use/land cover changes, ground water abstractions, watershed development and storage) may be attributed the stream flow declining trends as there is no dramatic changes in precipitation over the analysis period. A stream flow change without any change in rainfall was also reported by the study conducted by Nune et al. (2012). Furthermore, the decrease in the peak and mean river flows during the annual and wet seasons has critical implications for both the quantity and the quality of water available for domestic uses and livestock watering, which needs due consideration by the concerned bodies.

Relationship between stream flow and climate variability
The

Conclusions
In this study, the long-term trends in precipitation and stream flow were examined based on daily hydro-meteorological records in the Modjo river watershed using statistical methods. The correlation between precipitation and stream flow was also investigated on the annual and seasonal basis between 1981 and 2015. Based on the results of the analysis, the major conclusions of the study are as follows: (i) The trend analysis result clearly revealed that annual precipitation experienced nonsignificant trends. However, the mean and maximum annual stream flow trends behaves differently by showing significant down ward trend at 5% significant level, with a declining rate of 8.262 and 16.85 m 3 s − 1 per annum respectively in the study watershed. The dramatic declining trends of the river flow; likely seems to be a potential threat for water shortage in the watershed over the next few decades; (ii) During the analysis period, except monsoon (kiremt) season precipitation at Edjere station, seasonal precipitation trends were showed non-significant trend in most of the stations.
Conversely, mean and maximum stream flow during the main rainy season (kiremt) exhibited significant declining trends, with a rate of 6.528 and 14.45 m 3 s − 1 per year respectively; (iii) Trends for the annual and seasonal minimum (base flow) data were not significant in the same study period.
Moreover, the mean flow series during dry (bega) season in the same study period showed a significant weak increasing trend; with a rate of 0.06 m 3 s − 1 (7.3%), which has a positive advantage for submission.

Ethics approval and consent to participate
Not applicable since human participants was not involved in this research to evaluate health related outcomes.

Funding
This research study was supported by Jimma University, Jimma Institute of Technology (JiT).

Availability of the data and materials
The data is included in the manuscript.  Linear trend test for mean, min and max flow during kiremt, belg & bega months (1981-