1 Introduction

Evidences generated from empirical observations and climate model studies confirm that the occurrence and negative impacts of extreme weather events are increasing across the world due to global warming (IPCC 2014). Impacts are generally high in developing countries like Ethiopia, not only due to the low adaptive capacity in economic terms but also due to the poor understanding and limited scientific knowledge on the spatio-temporal variability of the climate system, both for current and future time scales (Conway and Schipper 2011; ACPC 2013). Currently, over 70% of the observed natural disasters across the world are caused by climate-related events, and most of these disasters are caused by extreme rainfall-related events (droughts and floods) (Wang et al. 2019). Changes are apparent on the timing, onset and cession dates, length of wet and dry spells, number of wet and dry days, wet day rainfall intensity and frequency of heavy and very heavy rainfall events (IPCC 2014). Most of the impacts from climate change on ecosystems, water resources and human livelihood systems are induced through these extreme rainfall events. Several studies confirmed that Ethiopia’s economy and food security condition, which are largely based on rain-fed agriculture, are highly sensitive to rainfall variability and extreme events. Although there are other socioeconomic and political factors, it is estimated that a 10% decrease in seasonal rainfall amount results in about 4.4% decrease in the national food production (Bewket and Conway 2007). Similarly, World Bank (2006) reported that the economic growth of Ethiopia fluctuates by as much as 38% due to rainfall anomalies and water resource variability. This is because the capacity of hydropower production and power supply to the non-agricultural sectors significantly declines due to rainfall variability. For example, in the 2002/2003 drought year, the GDP of the country declined by 10–15% per day for the days of power interruption (Conway et al. 2007). Human deaths, displacement, damage on field crops and infrastructure and outbreak of water-borne diseases were also reported in different parts of the country following riverine and flash flood events (World Bank 2006; Block 2008; Billi et al. 2015). The high cost of rainfall variability indicates that information on the spatio-temporal variability of rainfall amounts and extremes is vital for evidence-based policy and decision-making.

However, in Ethiopia and elsewhere in many African countries, there is very little or no scientific information about the spatio-temporal variability and trends in rainfall amount and extreme events to develop science-informed and evidence-based climate risk management and climate change adaptation planning (Conway and Schipper 2011; ACPC 2013). The absence of such information is largely attributed to the lack of long-term time series data, limited spatial coverage of available datasets and inadequate climate experts in the region (ACPC 2013). It is important to generate and communicate scientific information on the spatio-temporal variability of rainfall amount and extreme events preferably at local levels for designing evidence-based risk management and climate change adaptation planning.

In Ethiopia, most of the available studies were based on seasonal and annual rainfall amounts (Osman and Sauerborn 2002; Conway et al. 2004; Meze-Hausken 2004; Cheung et al. 2008; Visteet al. 2013; Mengistu et al. 2014), which largely mask important variations on extreme rainfall events. There are also few studies on extreme rainfall variability at country (Seleshi and Zanke 2004; Seleshi and Camberlin 2006) and regional scales (Bewket and Conway 2007; Rosell and Holmer 2007; Shang et al. 2011; Degefu and Bewket 2014; Mekasha et al. 2014). Results generated from these studies revealed non-systematic patterns of trends for all rainfall indicators, and trend signals are highly sensitive to the station/s or region and period of time considered in the analysis (Bewket and Conway 2007). Most of these studies have found local-based (station-specific) and contrasted statistically significant upward and downward trends for some rainfall indicators. This implies that the response of local climate to global climate change is different at different locations, and this further suggests the need for further studies to improve our understanding of rainfall variability and trends at local and regional scales using dense observation stations. It is important to note that the aforementioned studies used only few recording stations that ranged from one station per study area (e.g. Conway et al. 2004; Shang et al. 2011) to 12 stations (e.g. Bewket and Conway 2007), and the results generated from these studies cannot fully capture the spatial variability of trend signals for extreme rainfall events as rainfall over Ethiopia shows a large spatial variation with short distances due to complex topography (Degefu and Bewket 2014).

The aim of this study was to analyse the spatio-temporal variability and trends of rainfall amount and extreme event indices for the southeastern part of Ethiopia. This part of the country is found to the east of the Ethiopian Rift Valley, and it is characterized by a variable climate which is associated with the complex topographic features of the area. Part of this area such as the Arsi and Bale highlands are known for wheat and barley production; the south-central part in the Sidamo and Gedio area is known for coffee production, and the vast lowland part supports a pastoral livelihood system. Available evidence such as Pantuliano and Wekesa (2008), Rettberg (2010) and Ng’ang’a et al. (2016) indicated that rainfall variability is a leading and growing environmental problem in lowland drylands, causing frequent water and feed shortages to livestock and thereby affecting the pastoral livelihood systems. Both riverine and flash floods occur in the lowland areas of Ethiopia almost every year and cause frequent damage to field crops grown by irrigation, livestock and settlement areas along the major river courses (the rivers of Awash, Genale-Dawa and Wabe-Shebele) (World Bank 2006; Block 2008; Billi et al. 2015). Recently, the Government of Ethiopia has constructed hydroelectric power dams and medium-scale irrigation projects along many river systems that include Genale-Dawa, Wabe-Shebele and Awash rivers. The results generated from this study will therefore provide important empirical information on the spatio-temporal variability of rainfall amount and extreme events for policymakers, water resource managers and practitioners to develop effective climate risk management options and sustainable water resource management plans for the region.

2 Methodology

2.1 Description of the study area

This study covered the southeastern part of Ethiopia that extends between 3° and 10° 30′ N and 37° and 48° E (Fig. 1). The area is characterized by complex topographic features with extensive lowland plains in the eastern and southeastern parts and rugged mountains that extend from the south-central to northeastern parts. It is separated from the remaining part of the country by the Ethiopian Rift Valley system, which runs from the northeastern to southwestern parts of the country. This complex topography is further dissected by the two major river systems (Wabe-Shebele and Genale-Dawa) of the area that originate from the southeastern highlands and flow eastward towards the Indian Ocean. There are also many other small river systems (e.g. Ketar and Ashebeka) originating from the western part of the southeastern highlands and flowing towards the Rift Valley Lakes Basin system. The area covers more than one-third of the country’s area, and elevation varies between 166 and 4238 m a.s.l.

Fig. 1
figure 1

Topography and location of meteorological stations used in this study

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The climate of the area is characterized by very hot and dry conditions in the eastern and southern lowlands and relatively cold and wet conditions over the highland areas. The mean annual temperature ranges from less than 10 to over 40°C, and annual rainfall amounts vary from less than 300 to over 1500 mm. Over the lowland area, the rate of evapotranspiration is very high due to high atmospheric water demand. The lower rainfall amount together with the high rate of evapotranspiration results in severe scarcity of water resource over the lowland areas. Although not supported by empirical climate data, the lowland part of the region is frequently affected by drought and flood hazards. Floods occur due to localised heavy rainfall events (in the form of flash floods) and overflow of water from the major rivers that originate from highland areas (Awash, Genale-Dawa and Wabe-Shebele rivers). Droughts and floods significantly affect the livelihood of lowland communities by causing severe food and water shortages, mass livestock deaths, malnutrition and disease outbreaks (Pantuliano and Wekesa 2008).

Pastoralism and mixed farming (crop cultivation and livestock rearing) are the dominant livelihood systems in the lowland and highland parts of the region, respectively. The southern part of Afar in the Rift Valley system, the Somali area in the east and the Borena lowland in the southern part of the study area are mostly pastoral livelihood systems, keeping cattle, camel, sheep and goat. Wheat and barley are widely grown in Arsi and Bale highlands. Maize is also an important food crop grown over a large area in the region. Coffee in the south-central highlands particularly in the Sidamo and Gedeo areas and Chat or Khat (Catha edulis) in the Hararghe highlands are the important cash crops grown in the region.

2.2 Data and sources

Daily rainfall data for 44 recording stations were obtained from the National Meteorological Agency of Ethiopia (NMA) (Fig. 1). These stations cover the period between 1955 and 2015 with start years ranging from 1955 to 1985 and show a good spatial distribution to cover the study area. The density of these stations is relatively higher over the highland area and thus can have good representation to capture the spatial variability of rainfall amount and extreme events caused by the rugged mountainous topography. Over the lowland part, the density of stations is relatively low, but the few available stations can represent the lowland area as the spatial variability of rainfall in this area is considerably low.

2.3 Data quality control

All the data were checked for their quality of record length, missing data and inhomogeneity. In this regard, we rejected 18 out of 62 recording stations that we obtained from the NMA due to their short record length (< 30 years), missing data for extended years and inhomogeneity of the data series. The homogeneity of the data series was checked by the Standard Normal Homogeneity Test (SNHT) (Khaliq and Ouardab 2007). Stations with missing daily data for less than 15% of the records were maintained and filled in with data from neighbouring stations using the linear regression method after checking for their significant correlation at 0.05 level, otherwise were kept as missed. Table 1 presents description about the stations used in this study.

Table 1 Description of the meteorological stations used in this study
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2.4 Extreme rainfall indices

Table 2 presents description on extreme rainfall indices used in this study. Twelve extreme event indices were defined and generated from the daily time series based on WMO (2009) guidelines and other references (e.g. Mekasha et al. 2014). In this study, a wet day is defined as a day with rainfall greater than 1.0 mm, otherwise dry day. Then, extreme event indices were generated for the annual time scale and for the three wet seasons in the study area (March–May, June–September and September–November). All extreme indices were generated using Microsoft Excel software by climate experts.

Table 2 Definitions of the daily rainfall and extreme event indices used in the study
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2.5 Trend detection

The non-parametric Mann–Kendall trend test and Sen’s slope estimator were used to determine trends and estimate rates of change for all rainfall time series after all the data were checked for lag-one serial correlation. Although Mann–Kendall trend test is robust over the other parametric tests as it cannot be affected by data distribution, outliers and missing data (Kundzewicz et al. 2005), it tends to inflate the number of statistically significant positive trends than were actually present if there is significant serial correlation in the data time series (Yue et al. 2002; Burn et al. 2010). In this regard, we employed the most commonly used Prewhitening method to remove serial correlation before applying the Mann–Kendall trend test (Petrow and Merz 2009; Burn et al. 2010; Degefu and Bewket 2017; Degefu et al. 2019). Detailed explanations on the procedures of the Prewhitening method are found in Yue et al. (2002). The MAKESENS Microsoft Excel add-in software that is developed by the Finnish Meteorological Institute (Salmi et al. 2002) was used to detect trends at 0.05 and 0.1 significance levels. We also applied a simple global field significance test to check whether or not the observed trends for each rainfall indicator were statistically significant at the regional scale. Thus, the global field significance of trends for each rainfall indicator was calculated by comparing the number of locally significant trends in the region with that expected from chance at 0.05 and 0.1 levels. It is commonly used in hydroclimate trend studies (e.g. Burn et al. 2010; Degefu et al. 2019). The spatial patterns and variation of trends for each rainfall indicator are mapped using Geographic Information System (GIS). We used different types of symbols in different sizes and colours to show the patterns of trends whether the observed trend signal is an upward or downward and the level of significance for each station.

2.6 Rainfall variability analysis

We also calculated the long-term mean and coefficient of variation (CV) for annual and seasonal total rainfall time series. Furthermore, standardised rainfall anomalies (SRA) were calculated to show the year-to-year fluctuations of rainfall amount for the selected stations that have long record lengths. SRA were calculated as follows:

$$ \mathrm{SRA}=\left( Pt- Pm\right)/\upsigma $$

where SRA is the standardised rainfall anomaly, Pt is the annual rainfall in year t, Pm 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.

3 Results

3.1 Variability of annual and seasonal rainfall amounts

Table 3 presents a summary of mean rainfall amounts and CV for the areal average annual and seasonal time scales. The results on mean rainfall amounts, CV, inter-annual rainfall variability and spatial pattern of annual rainfall cycle confirmed the presence of very high spatio-temporal rainfall variability in the study area. The mean annual rainfall amount for the whole study area was 877.4 mm as calculated for the period 1970–2015. The CV was 13%. The mean annual rainfall amount was relatively greater over the north-central part (935.4 mm) and a little bit less over the southern part (819.4 mm) of the study area. In contrast, CV was relatively less (12.3%) over the north-central and high (17.6%) over the southern parts of the study area. Station-wise, the mean annual rainfall amount varied between 238.8 mm at Gode in the eastern lowland and 1892.6 mm at Jarso in the south-central highland part of the study area. Similarly, CV varied between 12.7% at Kulumsa and 63.8% at Kombolcha stations. Inter-annual rainfall variability as shown by the standardised rainfall anomalies (Fig. 2) was very high. The proportion of years with negative rainfall anomalies was relatively greater than that with positive anomalies at more than 85% of the stations considered in this study.

Table 3 Mean rainfall amounts and coefficient of variation for the areal average annual and seasonal time scales
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Fig. 2
figure 2

Standardised rainfall anomalies at selected rainfall stations

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From the seasonal cycles of rainfall, three wet and three dry seasons were identified (Fig. 3). The three wet seasons are March–May (locally known as belg), June–September (locally known as kiremt) and September–November (locally known as meher) (Table 3). The first one is wet season across the entire study area, while the second and the third wet seasons cover the northern and southern parts of the area, respectively. March–May is the main rainfall season for the southern and the secondary season for the northern parts that accounts for 35–58% and 15–38% of the total annual rainfall amount when considered for each individual station, respectively. The areal average March–May mean rainfall amount was 385.7 mm in the southern part and 281.1 mm in the north-central part of the study area and had 47.1% and 30.1% contribution to the annual total rainfall amount, respectively. June–September and September–November are the primary and secondary wet seasons for the northern and southern parts of the area that contribute around 44–74% and 28–46% of the total annual rainfall amount, respectively. The areal average mean rainfall was 511 mm for the former and 268.6 mm for the latter wet seasons; these had 54.6% and 32.8% contribution to the annual total rainfall amount, respectively. The periods between October and February in the northern part and between June and August and December and February in the southern part are dry seasons that account for 8.1–15.3%, 0.6–28.8% and 1.3–l1.1% of the total annual rainfall amount, respectively. The areal average mean rainfall amount was 143.3 mm for the October–February, 111.9 mm for the June–August and 53.1 mm for the December–February seasons, and these dry seasons had about 15.3%, 13.7% and 6.5% shares to the annual total rainfall amount, respectively (Table 3). CV variation is relatively less for the wet seasons (11.6–29.5%) and large for the dry seasons (34.7–74.5%). In addition to this, CV for annual and wet and dry seasons were relatively high over the southern part of the study area, except for the June–August dry season that showed lower CV (34.7%) as compared to the CV (46.4%) for north-central dry season (October–February).

Fig. 3
figure 3

Spatial variation in annual rainfall cycle in the southeast Ethiopia

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3.2 Trends of annual and seasonal rainfall amounts

Table 4 presents a summary of Mann–Kendall trend test results for the annual and seasonal rainfall amounts. The annual total rainfall time series showed decreasing trends at 26 out of 44 stations. Of these, the decreasing trends at 5 stations were statistically significant at 0.05 level. In addition to these, the downward trends at 9 stations were statistically significant at 0.1 level. The rates of these statistically significant downward changes varied between 27.5 mm/decade at Kofele and 97 mm/decade at Yirga Chefe. The observed decreasing changes were global field significant.

Table 4 Summary of trends for the annual and seasonal total rainfall amounts for 44 stations
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We also identified systematic trend patterns for the spatially different wet and dry seasons. The total rainfall amount for the March–May season showed decreasing trends at 32 out of 44 stations. Of these, the decreasing trends at 7 stations were statistically significant at 0.05 level. In addition to these, the downward trends at 10 stations were statistically significant at 0.1 level. The rates of these statistically significant downward changes varied between 22.3 mm/decade at Metehara and 75.6 mm/decade at Kulubi stations. The observed decreasing changes for the March–May season were global field significant. In contrast, the trend signals at 12 stations for the March–May season were upward, and none of these was global field significant. On the other hand, the trend test for the June–September rainfall amount over the northern part of the study area showed mixed global significant upward and downward changes (Table 4). The results showed upward signals at 17 and downward at 16 out of the 33 stations, and 3 of these trends for each of the upward and downward signals were statistically significant at 0.05 level. In addition to these, increasing trends at 7 stations had P < 0.1. The rates of these statistically significant increasing and decreasing changes varied between 23.5 and 150.7 mm/decade and 18 and 54.5 mm/decade, respectively. Different from the other two wet seasons, the rainfall amount for September–November over the southern part of the study area showed a global significant upward change. Increasing changes were found at 7 out of 11 stations, and 3 of these were statistically significant at 0.05 level. Statistically significant changes were observed at Gode (20.2 mm/decade), Aleta Wendo (54.5 mm/decade) and Dello Mena (77.4 mm/decade) stations.

On the other hand, the rainfall amounts for the three dry seasons (October–February, June–August and December–February) did not show global field significant trends. The trend test result for the October–February rainfall amount over the northern part of the study area was upward at 15 stations and downward at 18 stations. Only 2 of the decreasing trends were statistically significant at 0.05 and 0.1 levels. Two increasing trends had also P < 0.1. The December–February rainfall amount over the southern part of the study area showed increasing signal at nine out of 11 stations, but only 1 of these was statistically significant at 0.05 level, and two trends had P < 0.1. The trend test signals for the June–August rainfall amount were upward at 7 stations and downward at 4 stations, and none of these was statistically significant (Table 4).

The spatial distribution of trend signals for the annual and six seasonal rainfall time series is presented in Fig. 4a–g. The trend tests for most of the time series showed nonsystematic and mixed spatial patterns across the study area. However, the trend signals for March–May, which is the main rainfall season over the southern and eastern parts of the study area, showed decreasing trend signals. Of these, the decreasing trends at Aleta Wendo, Hagere Mariam and Kebri Dehar were statistically significant at 0.05 level. Similarly, the trend signals at most of these stations were downward for the annual and December–February rainfall amounts. In contrast, most (63.6%) of the stations over this area experienced upward trend signals for the September–November wet season and June–August dry season rainfall amounts. On the other hand, most of the upward signals for annual and March–May rainfall amounts were observed in the northern highland part of the study area. It is important to note that there were contrasted upward and downward trend signals between nearby stations for all time scales (Fig. 4a–g) that imply the presence of important local factors affecting the spatial distribution of rainfall in the region.

Fig. 4
figure 4

The spatial distribution of trend tests for seven time series. a Annual. b March–May. c June–September. d September–November. e October–February. f June–August. g December–February. Symbols represented trend signals and significant changes as follows: ( ) statistically significant increasing trend at 5% level (SS), ( ) statistically significant increasing trend at 5% < P < 10% levels (SS), ( ) statistically non-significant increasing trend (NSS), ( ) statistically significant decreasing trend at 0.05 level (SS), ( ) statistically significant decreasing trend at 5% < P < 10% levels (SS) and ( ) statistically non-significant decreasing trend (NSS)

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3.3 Trends in extreme rainfall events

Table 5 presents a summary of trend tests for 12 extreme rainfall indices. The trend tests for high rainfall amounts (RX1day, RX7day, RX30day and RX25mm) and heavy rainfall events (R10mm and R25mm) showed global significant downward trends, both at 0.05 and 0.1 levels. The trend tests for these high rainfall indices were negative at 59–65% of the stations. Of these negative trends, 5 stations for RX1day, RX30day and RX25mm, 3 stations for RX7day and 4 stations for R10mm and R25mm were statistically significant at 0.05 level. On the other hand, 19.2–34.6% of the downward trends had P < 0.1. The rates of these global significant changes were between 2.0 and 8.8 mm/decade for the RX1day, 5.7 and 9.6 mm/decade for the RX7day, 10 and 22.3 mm/decade for the RX30day and 11.2 and 76.6 mm/decade for the RX25mm. Similarly, heavy (R10mm) and very heavy (R25mm) rainfall events decreased at the rates of between 0.9 and 4.4 days/decade and 0.2 and 2.1 days/decade, respectively. In contrast, the trend signals at 18 stations for RX1day, RX7day and RX25mm, at 17 stations for RX30day and R25mm and at 15 stations for R10mm were upward, and none of these increasing changes was global field significant at 0.05 level. However, the trend tests for RX1day, R10mm and R25mm were statistically significant (P < 0.1) each at 4 stations, and these were global field significant. The rates of change were between 2.1 and 6.3 mm/decade for RX1day, 1.8 and 8.3 mm/decade for R10mm and 0.4 and 0.8 mm/decade for R25mm.

Table 5 Summary of trends in extreme rainfall events
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The spatial distribution of trend signals for high rainfall indicators is presented in Fig. 5a–f. As shown, there was no clear and systematic geographic pattern for all these high rainfall indicators. Mixed upward and downward trend signals were observed across the study area and even between neighbouring stations. The only exception is that all the statistically significant upward changes for high rainfall indices were observed at the highland stations. Statistically significant upward changes were found at Bale Robie for RX1day and RX7day time series. Similarly, the increasing changes in the RX30day at Nuraera and Jarso; the RX10mm at Koka Dam, Jarso and Nuraera; the R25mm at Bale Robie and Nazret and the RX25mm at Alemaya and Bale Robie stations were statistically significant at 0.1 level. On the other hand, we found statistically significant opposite trends between neighbouring stations. For example, Bale Robe and Agarfa, which are only 26 km apart by air distance, revealed statistically significant opposite trends for RX1day and RX7day.

Fig. 5
figure 5

The geographical distribution of trends for a RX1day, b RX7day, c RX30day, d R10mm, e R25mm and f RX25mm. Symbols represented trend signals and significant changes as follows: ( ) statistically significant increasing trend at 5% level (SS), ( ) statistically significant increasing trend at 5% < P < 10% levels (SS), ( ) statistically non-significant increasing trend (NSS), ( ) statistically significant decreasing trend at 0.05 level (SS), ( ) statistically significant decreasing trend at 5% < P < 10% levels (SS) and ( ) statistically non-significant decreasing trend (NSS)

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The summary of trend test results for the number of wet days (NWD, ≥ 1 mm), dry days (NDD, < 1 mm), maximum consecutive wet day (CWD) and dry day spell (CDD) lengths is presented in Table 5. Results show global significant mixed upward and downward changes for NWD, NDD and CWD. For CDD, only the increasing change was global field significant. Accordingly, trend tests showed decreasing signal at 25 stations for NWD and at 23 stations for CWD, and of the decreasing trends, 7 for the former and 6 stations for the latter indices were statistically significant at 0.05 level. In addition to these, downward trends at 8 stations for NWD and 7 stations for CWD had P < 0.1. The rates of decreasing changes at these stations varied between 1.9 and 8.7 days/decade for the NWD and 0.9 and 1.5 days/decade for CWD. On the other hand, trend tests at 19 stations for NWD and 21 stations for CWD were upward, and 4 of these upward changes for each of these indices were statistically significant at 0.05 level. The number of statistically significant increasing changes was 5 for CWD, if 0.1 significant level was considered. The rate of increasing change at these stations was estimated between 2.1 and 10.5 days/decade for NWD and 0.1 and 1.0 days/decade for CWD. On the other hand, results of trend tests for NDD and CDD were increasing at 25 stations and decreasing at 19 stations for each of these indices. Of the increasing changes, 7 for the former and 4 for the latter indices were statistically significant at 0.05 level. The statistically significant increasing changes were 8 for the NDD when 0.1 significance level was considered. The rates for these statistically significant increasing changes were in the ranges of 1.9 to 8.7 mm/decade for the NDD and 3.2 to 10 mm/decade for the CDD. Out of the decreasing trend signals, 4 for NDD and 2 for CDD were statistically significant, both at 0.05 and 0.1 levels. The rate for these statistically significant decreasing changes varied between 2.1 and 11 for the NDD and 2.2 and 2.5 mm/decade for the CDD.

On the other hand, the trend test for total wet day rainfall (PRECPTOT) amount showed a global significant decreasing change, both at 0.05 and 0.1 levels. Decreasing signals were found at 26 out of the 44 stations, and 6 of these downward changes were statistically significant at 0.05 level. Similarly, the decreasing change at 9 stations had P < 0.1. The rates of these statistically significant decreasing changes were in the ranges of 27.4 to 97.4 mm/decade. In contrast, the trend signals at 18 stations were increasing, and only 2 and 3 stations were statistically significant at 0.05 and 0.1 levels, respectively. The increasing change in PRECPTOT was not global field significant. On the other hand, trend test results for wet day rainfall intensity (SDII) showed mixed global significant upward and downward trends. In fact, trend test at most of the stations (61.4% out of the 44) showed decreasing signals, and 5 and 7 of these downward trends were statistically significant at 0.05 and 0.1 levels, respectively. On the other hand, the trend tests at 17 (38.6%) stations were upward, and 5 of these increasing changes were statistically significant, both at 0.05 and 0.1 levels. The rate of these significant decreasing and increasing changes varied between 0.3 and 1 mm/decade and 0.3 and 1.1 mm/decade, respectively.

Figure 6 a–f show the geographical distribution of trend signals for NWD, NDD, CWD, CDD, PRECPTOT and SDII. Similar to the other time series, there was mixed and no geographically distinct trend signal for these time series.

Fig. 6
figure 6

The spatial distribution of trend tests for a NWD, b NDD, c CWD, d CDD, e PRECPTOT and f SDII. Symbols represented trend signals and significant changes as follows: ( ) statistically significant increasing trend at 5% level (SS), ( ) statistically significant increasing trend at 5% < P < 10% levels (SS), ( ) statistically non-significant increasing trend (NSS), ( ) statistically significant decreasing trend at 0.05 level (SS), ( ) statistically significant decreasing trend at 5% < P < 10% levels (SS) and ( ) statistically non-significant decreasing trend (NSS)

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3.4 Trends of extreme rainfall events for the wet seasons

Trend tests on extreme rainfall events for three wet seasons (March–May, June–September and September–November) are presented in Table 6. The general pattern and magnitude of trend tests on the extreme rainfall events were different for the three wet seasons. For example, for the March–May season, all the extreme rainfall indices, except for NDD and CDD, showed decreasing trend at more than 65% of the stations. Of these decreasing trends, 9.1 to 25.2% were statistically significant at 0.05 or 0.1 levels. The rates of these statistically significant decreasing changes were estimated to be in the range of 2.2–75 mm/decade for RX1day, 4.7–25 mm/decade for RX7day, 13.1–53.5 mm/decade for RX30day and 6.2–39.9 mm/decade for RX25mm. Similarly, the rates of downward changes for NWD, CWD, R10mm and R25mm were estimated at 1.2–2.4 days/decade, 0.3–2.2 days/decade, 0.7–3.3 days/decade and 0.3–0.9 days/decade, respectively. The rates of downward change for PRECPTOT and SDII varied between 22.1 and 70.1 mm/decade and 0.3 and 1.7 mm/decade, respectively. All these decreasing changes were global field significant. In contrast, the number of stations that showed increasing trend signals for the above rainfall indices ranged from 12 to 17 stations, and none of the upward changes was global field significant. Different from the other rainfall indices, trend tests for the number of dry days (NDD) and maximum dry spell length (CDD) were global field significant. Increasing trend signals were found at 28 stations for NDD and 25 stations for CDD, and 5 of these for the first and 3 for the latter were statistically significant at 0.05 level. In addition to these, 6 of the upward trends for both the indices had P < 0.1. At these stations, the rates of increasing changes were estimated at between 1.2 and 2.4 days/decade for NDD and 1.4 and 5.0 days/decade for CDD. In contrast, trend tests at 16 stations for NDD and 19 stations for CDD were downward; of these decreasing changes, only 1 station for the former and 2 stations for the latter were statistically significant at 0.05 level.

Table 6 Summary of trend tests in extreme rainfall events for the three wet seasons
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On the other hand, trend tests in extreme rainfall events for the main wet season (June–September) over the northern part of the study area showed global significant mixed increasing and decreasing changes (Table 6). Of course, except for CDD, most of the stations (48.5–60.6%) revealed an increasing signal, while the trend tests in the other 39.4–51.5% of the stations were decreasing. The trend test for CDD was upward at 12 stations and downward at 21 stations. In general, 3 to 6 of the increasing and decreasing trend signals for most of the extreme indices were statistically significant at 0.05 level. In addition to these, 3–8 of the increasing and decreasing trends for all extreme indices were statistically significant at 0.1 level (Table 6). The rates of statistically significant increasing changes were in the ranges of 2.6–7.5 mm/decade for RX1day, 4.0–13.8 mm/decade for RX7day, 8.1–44.6 mm/decade for RX30day and 13.6–65.3 mm/decade for RX25mm. Similarly, the rates of upward changes for NWD, CWD, NDD and CDD were in the ranges of 1.4–8.2 days/decade, 0.2–0.8 days/decade, 1.1–4.5 days/decade and 0.8–1.6 days/decade, respectively. The rates of upward change for R10mm and R25mm varied between 0.7 and 6.8 days/decade and 0.3 and 3.0 days/decade, respectively. Similarly, the rates of increasing changes for PRCPTOT and SDII were in the ranges of 15.4 to 150.5 mm/decade and 0.3 to 1.4 mm/decade, respectively. On the other hand, the rates of statistically significant decreasing change were in the ranges of 1.3–6.6 mm/decade for Max1day, 19–5.7 mm/decade for Max7day, 6.1–19.7 mm/decade for Max30day and 5.1–26 mm/decade for RX25mm. Similarly, the rates of downward change for NWD, CWD, NDD and CDD were in the ranges of 1.1–4.5 days/decade, 0.1–1 days/decade, 1.4–8.2 days/decade and 0.4–3.5 days/decade, respectively. Heavy (R10mm) and very heavy (R25mm) rainfall events declined at rates that varied between 0.7 and 2.1 days/decade and 0.4 and 0.8 days/decade, respectively. For PRCPTOT and SDII, the rates of downward change varied between 18.8 and 61.4 mm/decade and 0.2 and 0.6 mm/decade, respectively.

On the other hand, most of the extreme rainfall time series during the secondary rainfall season (September–November) over the southern part of the study area showed upward tendencies. Except for NDD and CDD indices, all the extreme rainfall indices showed increasing signal at 54.6–81.8% of the stations; however, very few of the increasing changes (1–2) were statistically significant at both 0.05 and 0.1 levels for most of the indices (Table 6). Only for three indices (NWD, R25mm and PRCPTOT) the increasing changes were global field significant. The rates of these significant increasing changes varied between 2 and 4.1 mm/decade for NWD, 0.3 and 1.3 mm/decade for R25mm and 20.4 and 78.1 mm/decade for PRCPTOT. In contrast, trend tests at 9 stations for NDD and 7 stations for CDD were downward. Of these, the decreasing change at 4 stations for the NDD was global field significant at 0.1 level. For the other extreme rainfall indices, decreasing trend signal was found at 2 to 5 stations, but only the decreasing change for RX1day was global field significant. The rate of decreasing change for RX1day was in the range of 1.7 to 4 mm/decade.

4 Discussion and conclusion

This is the first study that provides comprehensive empirical evidence on the spatio-temporal characteristics of rainfall amount and extreme events using daily data from irregularly distributed 44 recording stations for the southeastern part of Ethiopia, where rainfall variability, drought and flood are leading environmental hazards affecting crop farming, pastoral livestock rearing, water availability and human livelihood systems (Conway and Schipper 2011; Few and Tebboth 2018).

Results generated from this study demonstrate that there is significant spatial variation in rainfall amount, inter-annual variability, rainfall regime and trend patterns. For example, the mean annual rainfall varied between 238.8 mm at Gode in the eastern lowland and 1892.6 mm at Jarso station in the south-central highland. We found two spatially different bimodal annual rainfall regimes: March–May and September–November in the southern part and March–May and June–September in the northern part. March–May and June–September are primary wet seasons, while September–November and March–May are secondary wet seasons for the southern and northern parts of the area, respectively. The periods between these wet seasons are dry. The spatial variation in the rainfall amount and annual rainfall regime is attributable to altitudinal variation and the north-south migration of the Intertropical Convergence Zone (ITCZ) across the study area (Gamachu 1988; Segele et al. 2009; Degefu et al. 2017).

Trend tests computed for annual and seasonal total amounts showed some systematic patterns of change. The trend tests at 60% of the stations for annual and 72.7% of the stations for the March–May season showed downward signals. Of these, the downward trends at 19.2% of the stations for the first and 21.9% for the second were global field significant at 0.05 level. The proportions of global significant trends at 0.1 level were 34.6% for the annual and 31.3% for March–May. Trend tests for the June–September season revealed mixed upward (51.5%) and downward (48.5%) signals. Of this, more than 17% of trend signals for both upward and downward changes were global field significant. The proportion of stations that showed global significant increasing trend at 0.1 level was 41.2%. Trend test for September–November was increasing at 7 out of 11 stations that represent the southern part of the study area. Of these, increasing trends at 3 stations were global field significant at 0.05 level. No global significant change was observed for the dry seasons.

Similarly, results of trend tests for extreme rainfall indices showed different change patterns across the three wet seasons. The trend tests for the March–May season showed global significant decreasing trends for all indices, except for NDD and CDD, which showed global significant increasing tendency. For the June–September season over the northern part of the study area, both global significant upward and downward trends were found for all rainfall indices. Although there were few significant trends, most of the indices except NDD and CDD showed upward signals for the September–November season over the southern part of the area. The downward trends in NDD and CDD over this area were global field significant. For the annual time scale, all the high rainfall indicators (RX1day, RX7day, RX30day, RX25mm, R10mm and R25mm) and total wet day rainfall amount (PRCPTOT) showed decreasing signal at 60–65% of the stations. Of these, decreasing changes at 14.8–28% of the stations were global field significant at 0.05 level. On the other hand, the trend tests for NWD, NDD, CWD and SDII showed mixed global significant upward and downward trends.

We found some discrepancies between our study and previous studies. For example, the mixed global significant upward and downward trends that we found for the June–September season did not coincide with those studies that reported statistically significant decreasing trends for the same area for the periods 1962–2002 (Seleshi and Zanke 2004) and 1971–2010 (Viste et al. 2013). Cheung et al. (2008) also reported the absence of significant trend for this season for the period 1960–2002. Similarly, Mekasha et al. (2014) reported an absence of significant trends for nine extreme event indices considered at 11 stations for the period 1967–2008, except that this study found statistically significant decreasing trend at the Neghele station for some rainfall indices. Our findings also disagree with the absence of significant trends reported for maximum consecutive dry spells (days with rainfall less than 1 mm), both for March–May and June–September seasons for our study area for the period 1962–2002 (Seleshi and Camberlin 2006). This study also found statistically significant decreasing trend in extreme rainfall intensity for June–September and increasing trend in March–May rainfall amount for the same period for the southeastern part of Ethiopia. On the other hand, none of the previous studies generated rainfall trends for the secondary (September–November) rainfall season over the southern part of Ethiopia. In general, much of the observed discrepancies are attributable to the variations in the number (density) of gauging stations and length of record period used in the trend analysis for this region (Bewket and Conway 2007; Conway and Schipper 2011).

However, the trend results we found for some rainfall indices and time scales are in line with rainfall trends reported for this area by some previous studies (e.g. Verdin et al. 2005; Funk et al. 2008; Viste et al. 2013). These studies reported the presentence of statistically significant decreasing trends for annual and March–May total rainfall amounts. Seleshi and Camberlin (2006) also reported statistically significant decreasing trends in extreme intensity, maximum consecutive 5-day and extreme high-frequency rains both for March–May and June–September seasons for the period 1962–2002 but only for two recording stations (Neghele and Jijiga). The decreasing March–May rainfall amount and other heavy rainfall indicators could be attributed to the impact of global warming over the Indian Ocean (Verdin et al. 2005; and Funk et al. 2008). These studies reported the development of increasing sea surface temperature over the Indian Ocean particularly during the boreal spring, which reduces moisture transport towards the Greater Horn of Africa by increasing convection over the ocean and producing surface wind anomalies.

In general, our study has generated important and up-to-date information on rainfall and extreme event trends using dense recording stations that very likely represent the multiple microclimate conditions in the study area. It is unique as it generates and provides trend information in rainfall amount and extreme event indices for the three spatially distinct wet seasons, namely, March–May, June–September and September–November, where the latter was not considered in all previous studies. Thus, the trend results generated for these three seasons provide useful information to understand the possible impacts that emerge from rainfall changes and to design appropriate adaptation strategies for specific season and local contexts. For example, the decreasing trend in March–May rainfall, which is the main rainfall season over the south and eastern parts of the study area has significant negative impacts on the traditional livestock rearing and pastoral livelihood systems as it causes severe shortage of water and pasture availability (FAO 2010; Few and Tebboth 2018). The observed statistically significant increasing trends in annual and June–September rainfall amounts and other high rainfall indices over highland parts indicate the need to develop flood management strategies over lowland areas (World Bank 2006; Block 2008; Billi et al. 2015). On the other hand, the apparent mixed global significant upward and downward trend signals for the June–September season suggest the need to local-specific climate change adaptation strategies.