Analysis of spatial variability and temporal trends of rainfall in Amhara region, Ethiopia

Understanding rainfall distribution in space and time is crucial for sustainable water resource management and agricultural productivity. This study investigated the spatial distribution and temporal trends of rainfall in Amhara region using time series rainfall data of Climate Hazards Group Infrared Precipitation with Stations (CHIRPS) for the period 1981 – 2017. Coef ﬁ cient of variation, standardized anomaly index (SAI), precipitation concentration index (PCI) and seasonality index (SI) were used to evaluate rainfall variability and seasonality. Mann – Kendall ’ s test was also employed for rainfall trend analysis. Results showed that the region has been experiencing variable rainfall events that cause droughts and ﬂ oods over different years. SAI also witnessed the presence of inter-annual variability of rainfall with negative and positive anomalies in 59.46% and 40.54% of the analyzed years, respectively. PCI and SI results implied that the area had irregular and strong irregular rainfall distribution. Trend analysis results showed an overall increase in the annual and seasonal rainfall (except winter) during the study period. The information obtained from this study could serve as a proxy for rainfall variability and trend in the study area which might be used as input for decision-makers to take appropriate adaptive measures in various agricultural and water resources sectors. Understanding rainfall distribution in space and time is crucial for


INTRODUCTION
Climate change and variability are perceived as being the greatest threats to agricultural production and food security in sub-Saharan African countries, particularly for regions that depend on rain-fed agriculture (Kisaka et al. ). Ethiopia, like other countries in the region, is highly exposed to climate change and variability and has experienced several food crises during the last decade (Viste et al. ). Rainfall is one of the most important climatic variables that has a direct and indirect impact on agricultural production and ecosystem health (Weldegerima et al. ). Erratic rainfall patterns and frequent extreme events such as droughts, floods and irregularities in seasonal rainfall amount and distribution are among the major climate-related catastrophes that have drastic ramifications on food security and economic growth (Cattani et al. ).
Analysis of the spatial distribution and the temporal trends of rainfall is crucial for water resource management, agricultural productivity and climate change mitigation (Ayalew et al. ). Moreover, analyzing both inter-annual and intra-annual trends in rainfall offers intuitive information on the dynamics of soil moisture in rain-fed systems (Zhao et al. ). Such spatial and temporal trend analyses of rainfall require long-term rainfall time series data at high temporal and spatial resolutions. Traditionally, meteorological stations have been used as the main source of rainfall data. However, the use of meteorological stations for rainfall monitoring is less applicable in most parts of the world, especially in less developed countries in which the stations are typically sparse, poorly spatially distributed, and have data discontinuities (Kimani et al. ). This is also true in Ethiopia, particularly in Amhara regional state, where this study was conducted. The majority of previous studies have been confined to data from a few meteorological stations, and are therefore spatially incomplete. In recent decades, satellite-derived rainfall products have been used for providing rainfall estimates on global scale at ever increasing spatial and temporal resolutions as a viable alternative to station observations (Cattani et al. ; Dinku et al. ). Moreover, satellite-derived rainfall estimates provide timely, repetitive, and cost-effective information about rainfall at different time scales from daily to annually, which makes them very crucial, particularly in drought monitoring and early warning systems (Toté et al. ; Muthoni et al. ).
However, there are uncertainties associated with techniques for satellite rainfall estimates. The uncertainties may arise from spatio-temporal sampling errors, error from algorithms, and satellite instruments themselves (Gebremichael et al. ). These may affect the accuracy of satellite-derived rainfall estimates and may result in a significant error when they are used for different applications such as rainfall pattern and variability study.
Thus, the reliability of the satellite-derived rainfall products need to be evaluated before using them for the intended applications.
Nowadays, there is a wide variety of satellite-based rainfall products derived from multiple data sources. Climate

Hazards Group InfraRed Precipitations with Stations
(CHIRPS) is a relatively new rainfall product with high temporal and spatial resolution, and is based on multiple data sources. CHIRPS provides long-term datasets (from 1981 onwards), which can be profitably exploited for the evaluation of rainfall trends. Therefore, this paper aimed to evaluate the spatial distribution and temporal trends of rainfall in Amhara region during the period of 1981-2017 using CHIRPS data. Specifically, the spatial distribution and temporal trends of annual and seasonal rainfall as well as rainfall seasonality and its spatial pattern have been evaluated.

Study area
The Amhara region ( Figure 1) is located in the northwestern and northcentral parts of Ethiopia. Geographically, it lies between 9 20 0 and 14 20 0 N latitude and 36 20 0 and 40 20 0 E longitude. Its area is estimated at about 170,000 square kilometers and is divided into 11 administrative zones. Elevation ranges from 700 m to 4,620 m a.s.l. The area with the lowest elevation is located in the western Amhara, whereas high elevations are in the eastern and northeastern regions. Most of the region is on the highland plateau above 1,500 m and is characterized by rugged mountains, hills, valleys, and gorges. The livelihoods of the majority of the populations in the region are highly dependent on rain-fed agriculture. The region is characterized by erratic rainfall, high land degradation, and high rate of poverty (Ayalew et al. ). Erratic rainfall patterns and frequent extreme events cause crop failure and threaten the food security and livelihoods of the people in the region.
Therefore, knowledge of the spatial and temporal variability of rainfall patterns in the region helps the local community to better plan sustainable adaptation and mitigation strategies and secure sustainable agricultural production.

Meteorological stations' data
Monthly rainfall data were collected from eight meteorological stations (Table 1)

Validation statistics
In this study, the evaluation of the satellite rainfall products has been carried out for the period from 2000 to 2010 using and gauge rainfall. It is given by the equation where G i is gauge rainfall amount, G mean gauge rainfall amount, S i is satellite rainfall estimates, S is mean satellite rainfall estimates, and n is total number of data.
The mean error (ME) defined by the equation  is the measure of average difference between satellite and gauge rainfall amounts. A positive value reflects an overestimation of satellite rainfall whereas negative value indicates underestimation of satellite rainfall.
The mean absolute error (MAE) measures the average magnitude of the absolute value difference between satellite and gauge rainfall amounts. It is calculated using the for- Percent bias (PB) measures the average tendency of estimated values, which can either be larger or smaller than their observed ones, with an optimal value of 0. It can be cal-

Rainfall variability and trend
The annual, seasonal, and monthly CHIRPS rainfall time  (Douglas et al. ). Thus, in this study, rainfall variability has been computed using CV, SAI, PCI, and SI. Moreover, MK test and Sen's slope estimator were applied to detect and quantify possible trends in the time series data.

Coefficient of variation
The coefficient of variation measures the overall variability of the rainfall in the area of interest. A higher value of CV indicates a rainfall greater variability and vice versa. It is computed using the formula where σ is the standard deviation and μ is the mean rainfall for the chosen temporal scales. Generally, CV is used to classify the degree of variability of rainfall events into three: low (CV < 20), moderate (20 < CV < 30), and high

Standardized anomaly index
Standardized anomaly index of rainfall has been calculated to examine the nature of the trends. It enabled the determination of the dry and wet years in the record and is used to assess frequency and severity of droughts and it is computed as: where X i is the annual rainfall of the particular year; X is the long-term mean annual rainfall over a period of observation and σ is the standard deviation of annual rainfall over the period of observation. Negative values indicate a drought period as compared to the chosen reference period while the positive ones indicate a wet situation. SAI is also computed for seasonal scale. SAI value classification is presented in Table 2.

Rainfall seasonality
To evaluate seasonality of rainfall, PCI and SI were used.
The PCI indicates the distribution of monthly rainfall and can be used as an indicator of hydrological hazard risks such as floods and droughts (Gocic et al. ). PCI was calculated on an annual scale for each grid point according to the equation where P i is the monthly precipitation in month i. SI is an index which helps to identify the rainfall regimes on the monthly distribution of rainfall. Moreover, this index quantifies the degree of variability in monthly rainfall through the year. The higher the seasonality index of a region the greater the water resource variability and scarcity in time, the more vulnerable the area to desertification. SI is simply the sum of absolute deviations of mean monthly rainfall from the overall monthly mean, divided by the mean annual rainfall. The computation of SI is done using the where, P i is the mean rainfall (mm) of the i th month, and P is the mean annual rainfall (mm). The index varies from zero, if all the months have equal rainfall, to 1.83 if all the rainfall occurs in a single month. Table 3 shows the different class limits of SI and representative rainfall regimes (Kanellopoulou ).

Serial autocorrelation test
In order to avoid the influence of serial autocorrelation on the MK trend test, the serial autocorrelation should be checked before applying the MK trend test. To check the presence of a significant autocorrelation, correlograms and autocorrelation function (ACF) at lag 1 were used. Lag 1 ACFs were computed using the formula where r 1 , X i and X are the correlation coefficient at lag 1, rainfall time series, and mean value of the rainfall time series, respectively. The confidence interval of r 1 at the 5% significance level can be computed as procedure that takes serial dependence into account.
When serial dependence is absent, the MMK trend test is where n is the length of the dataset, x i and x j are two elements of the considered time series at the time step i and j, respectively, and If the dataset is identically and independently distributed, then the mean of S is zero and the variance of S is given by where n is the length of the dataset, m is the number of tied groups (a tied group is a set of sample data having the same value) in the time series and t i is number of data points in the i th group.
The Z statistics is computed using the formula A significant level α is also utilized for testing either an upward or downward monotone trend.

Validation results
The performance metrics results of the comparisons between rain gauge measurements and CHIRPS data at both monthly and annual scales for the period 2000 to 2010 are shown in Table 4. Good agreement between the station observations and CHIRPS rainfall data was observed with correlation coefficients R ¼ 0.91 and R ¼ 0.86 for monthly and annual scales, respectively. The negative values of ME and PB in both temporal scales indicated that the CHIRPS data tended to slightly underestimate the observed rainfall data. In general, the performance metrics revealed that better agreement between rain gauge measurements and CHIRPS data was observed in the monthly scale than the annual scale, and further validation results were presented using the monthly scale.
In addition to performance metrics, Figure 2 Table 5. As can be seen from the To see the effects of elevation variability on the performance of CHIRPS rainfall estimates, stations with a broad range of elevations from 790 to 2,980 m a.s.l were used.
The results of the performance metrics obtained by comparing rain gauge measurements and CHIRPS rainfall data for each station at monthly time scale are presented in Table 6.
The correlation coefficients ranged from 0.88 to 0.94, indicating good agreement between CHIRPS rainfall estimates and rain gauge observations at both high and low elevations.
Results of ME and PB revealed that CHIRPS rainfall estimates tended to underestimate rain gauge observations at low elevations. In general, from the values of R it can be inferred that CHIRPS product performed better at a low   Overall, the results of this validation study have shown the potential of CHIRPS rainfall product to be used for various applications such as rainfall pattern and variability study in Amhara region.

Rainfall summary statistics
Rainfall characteristics, such as mean, standard deviation (SD), CV, and percentage contributions of monthly and seasonal rainfall to annual rainfall were computed for the period 1981 to 2017 over the study area and the results are presented in Table 7.

Variability and anomalies of rainfall between 1981 and 2017
The coefficient of variation of the annual rainfall (21.13%) revealed moderate inter-annual variability of annual rainfall over the study area. Similarly, July and August had moderate rainfall variability (10 < CV < 30). The remaining months had coefficients of variation between 30% and 75%, indicating higher rainfall variability in these months. Similarly, higher rainfall variability was observed in all seasons except summer (JJA). Although annual rainfall showed moderate inter-annual variability, seasonal rainfall (except summer) showed comparably higher coefficient of variation, implying much larger variation in the seasonal rainfall between the years. Moreover, the CV of winter rainfall (52.08%) was higher than that of summer rainfall (19.39%), which implied more inter-annual The spatial distribution of the coefficient of variation of the annual rainfall in the study area is shown in Figure 5.
The CV varied from 6.42% in the southwestern part of the study area to 20.18% in the northeastern part of the study area. Areas with high annual rainfall indicated less interannual variation whereas areas with low annual rainfall showed moderate inter-annual variation. The moderate inter-annual variability in low rainfall areas indicated that comparably there was a greater contrast in annual rainfall values from year to year, and it suggested that in such areas, water availability became somehow more unpredictable as compared to areas with low CV.    (Table 7), even without the support of the significance.   Figure 10 illustrates the spatial distribution of SI in the Amhara region. The minimum SI values (0.64) were observed in the southeastern part of the study area whereas the maximum values (1.14) were observed in the north and northwestern parts of the study area.

Rainfall seasonality
The area (in percentage) of the different classes of SI of the study area is presented in Table 9. As observed in the

Trend analysis results
Examination of the autocorrelation function for annual rainfall time series did not reveal any significant serial correlation at all lags at the 95% confidence limit (Figure 11), enabling MK test to be applied without any further modifications. Following the serial correlation test, the MK test and Sen's slope estimator were applied to the rainfall time series data from 1981 to 2017 for Amhara region.
The trend analysis results, including the Z value from the MK test and the trend's slope (β) from Sen's estimator are  presented in Table

CONCLUSIONS
The availability of high spatial and temporal resolution satellite-derived rainfall products at local and global scales has proved to be valuable in complementing ground-based datasets, especially in developing countries that have data scarcity. This study has presented a detailed analysis of the spatial and temporal variability and monotonic trends of rainfall in Amhara region using CHIRPS rainfall data for a period of 37 years . The mean annual rainfall of the region was 1, 110:81 mm with standard deviation    whereas the SI varied from 0.64 to 1.14. From the analysis of these indices (PCI and SI), it can be inferred that most of the study area was characterized from seasonal to high seasonal rainfall distribution with longer drier season. The trend analysis presented both downward and upward trends depending on the chosen temporal scales. There was an overall increase in the annual and seasonal rainfall (except winter) in the study area during the study period.
The present study has offered useful information to better understand the spatial distribution and temporal trends of rainfall in the study area, which is of great importance for management of water resources and securing sustainable agricultural production. However, more comprehensive study on the driving forces of the trends and better validation options are required in the future.