Impact of climate change on the water resources of the Atbara River using novel hydrological models

Climate changes affect many areas of nature, humans, and society (Abbass et al. 2022). It is one of the most attractive areas of research in both the historic and future years, specifically, the impact of climatic factors on the hydrology of rivers and the hydrological cycle that affects the spatiotemporal distribution of water resources (El-Mahdy 2022). Therefore, this research focused on the influence of climatic conditions on the Atbara River, which is one of the main tributaries of the Nile River. It forms a part of the general flows of the Nile River. Climate change may affect the amounts of rain in the short and long term, affecting water availability and increasing droughts and floods (Mohamed & El-Mahdy 2021b). This problem may have a serious impact on Egypt. The Atbara River represents approximately 13% of the total discharge of the Nile River.

The impact of Climate Change on Hydrological Regimes and Water Resources Management in the Rhine Basin was investigated by Middelkoop et al. (2001). The effects of climate change on the drainage system in different areas of the basin were calculated. All models indicate the same trends in changes: higher winter discharge rate as a result of intense snowmelt and increased winter precipitation, and decreased summer discharge due to lower winter snow storage and increased transpiration. When the results were considered in more detail, many differences emerged. These can be first attributed to the different physical properties of these regions, but the different spatiotemporal scales used in the modelling and the different representations of many hydrological processes (e.g., evaporation, snowmelt) are responsible for the differences found as well. Ozkul (2009) assessed climate change effects in Aegean River Basins: the case of Gediz and Buyuk Menderes Basins. It showed that the global climate system is certainly warming. Observations showed that many natural systems, such as hydrological systems and water resources, are affected by climatic changes, especially the rise in temperatures. The simulation of the water budget model showed that approximately 20% of the surface water in the studied basins will be reduced by 2030. This percentage will increase to reach 35% and more than 50% in 2050 and 2100, respectively. Decreasing the surface water potential of basins will lead to serious water stress problems among water users.

Yates & Strzepek (1998) developed a model for the Nile Basin under climatic change. The subject of this research is the application and development of the Nile River Basin Monthly Water Balance Model (WBNILE) to determine the extent of the effects of potential climate changes on the Nile River discharges. This model consists of the 12 sub-regions in the Nile, including the lake region in tropical Africa and the basins in western Sudan. This model uses the method of averages of climate variables for each month, temperature, precipitation, hours of sunshine, relative humidity, etc., and the discharges for each part of the Nile River Basin. Precipitation changes and average temperatures were used, and five global circulation models (GCMs) were constructed for each sub-basin to assess the effects of climate variability and change on the discharges of the Nile River Basin. These results showed that the basin is affected by climate fluctuations because four models of the Earth cycle expected a significant impact, where there will be much larger flows than usual in tropical Africa and an increase in the area of swamps located in West Africa. Water balance modelling for the Nile basin has been studied by many researches (Abdelwares et al. 2019; El-Mahdy et al. 2021). Shiferaw et al. (2018) tested hydrological response under climate change scenarios using the Soil and Water Assessment Tool (SWAT) model: the case of the Ilala watershed, Northern Ethiopia. This research investigated runoff under variability and climate change scenarios for the Ilala watershed in the northern highlands of Ethiopia. The forms of climate change were studied and analysed using the delta minimization method based on representative concentration pathway (RCP) 8.5 and 4.5. It was found that nearly 75% of the total precipitation was lost as evapotranspiration and 7.8% as groundwater recharge. Due to increasing temperatures and evaporation in the future, runoff also begins to decline from 1.74% in the scenario RCP 4.5 to 0.36% in the scenario RCP 8.5 periods. The effect of both human and environmental factors on discharges of the Nile River was introduced in many studies (Keith et al. 2014). More than 33 circulation models (GCMs), including RCP 4.5 and 8.5, were investigated to model the relationship between climate change and discharges of the Nile River Basin. The temperature will rise significantly and continuously in all areas that have been assessed for the Nile River Basin during this century (Mohamed & El-Mahdy 2021a). Some studies found that rainfall is expected to increase the actual discharge amounts of the river (Malede et al. 2022). In other parts of the world, such as India, climate change has major effects on river hydrology. Guhathakurta & Rajeevan (2008) studied the trends of annual, monthly, and seasonal rainfall for a period exceeding 100 years from 1901 to 2003 in various parts of India. It indicated decreasing rainfall trends in the eastern and central regions. Murumkar and some other scientists conducted a study in 2014 on the analysis of trends and frequency in the form of precipitation for the stations of Bhor, Akluj, Baramati, and Malsiras in the Nera basin in central India. It was found that the seasonal rainfall in the summer season and winter season has a downward trend. They also found increasing trends in the annual precipitation rate of 10% for the two Bhuru Akluj stations (Murumkar & Arya 2014). There are many hydrological and statistical models for the Nile River and its tributaries, and they are often quite complex. Therefore, in this study, simplified and advanced models were made using different climate factors to study their impact over a long period of time on river discharges. The current study was conducted to achieve the following objectives:

• 1.

  Analysis of the factors affecting the hydrology and water resources of the Atbara River (precipitation, temperature, wind speed, relative humidity, and radiation) and their effect on the behaviour of the Atbara River.

• 2.

  Analysis of the changes in the monthly and the annual rainfall data.

• 3.

  Modelling the current and historical situations of hydrology and water resources of the Atbara River using novel statistical models.

• 4.

  Predicting the future hydrology of the Atbara River.

The site is located on the Upper Atbara and Setit rivers, about 20 km upstream from the confluence of the two rivers, 80 km south of the Khashm el-Girba reservoir, and 30 km from the city of Shawak. The project consists of two dams with a total length of 13 km and a lake with a storage capacity of about 3.7 billion cubic meters (BCM). The project includes the construction of two connected dams on the Upper Atbara and Setit rivers. The project includes an electric power plant located in the Upper Atbara Dam, which produces 320 mega watts (MW) (Ali 2017).

Khashm el-Girba Dam is a concrete dam located on the Atbara River, west of the city of Khashm el-Girba, 560 km east of the city of Khartoum, and 438 km from the city of Atbara as shown in Figure 1. The main objective of the Khashm el-Girba reservoir is to irrigate 450,000 feddans in the new Halfa Agricultural Project.

This station is located 3 km before the confluence of the Atbara River with the main Nile. The discharges of the Atbara are measured regularly on a straight uniform reach of the river at a point 3 km above its mouth, and a gauge is established at the site. Discharges were first measured during the floods of 1902 and 1903 then again in 1913, and the series began in 1921 and has been continued without interruption to the present day.

Climatic data such as monthly precipitation, maximum and minimum temperatures, humidity data, water deficit, wind speed, and other climatic factors were collected for the stations of Upper Atbara, Khashm el-Girba, and Atbara Kilo 3 in the Atbara River region. Also, data on hydrology (surface water) were collected.

The data of the measurement station used in this study for each month, as shown in Table 1, are taken from the reports of the Nile Basin Encyclopedia (Institute 2020).

The meteorological data used in this study for each month of the year were freely downloaded from the Internet link: https://climate.northwestknowledge.net/NWTOOLBOX/formattedDownloads.php?fbclid=IwAR2sLTy82aZRA_3iEHdd5N_r-bE1QJEiEKns3JsJ5Y0t1J19Qu1mOWC-eg. These data include the following:

• 1.

  Maximum monthly air temperature

• 2.

  Minimum monthly air temperature

• 3.

  Mean monthly wind speed

• 4.

  Mean monthly precipitation

• 5.

  Mean monthly runoff

• 6.

  Mean monthly solar radiation

• 7.

  Mean monthly climate water deficit

• 8.

  Mean monthly actual evapotranspiration.

GCMs can provide us with future projections of the climate. These data could be used by the international community to put in place mitigation measures for the projected climate change (El-Mahdy et al. 2021). Regional climate downscaling gets its importance from introducing projections of fine resolution for localized extreme events (Majone et al. 2022). Regional climate models (RCM) and empirical statistical downscaling applied over a small area and resulting from GCMs can supply information on a finer spatial resolution that energized more detailed studies in many parts worldwide. The projected meteorological data utilized in this study for each month from January 2022 to December 2050 were taken from CORDEX RCMs. CORDEX RCMs were recommended for projecting Africa's future climate (Mbaye et al. 2018). The data used in the study incorporate two CORDEX output scenario datasets: RCP 4.5 and 8.5 future emissions scenarios using the model CNRM-CM5 and can be freely downloaded from the Internet link: https://esgf-node.llnl.gov/search/cmip5.

RStudio is an integrated development environment for statistical package (R). It includes a console and syntax highlighting editor that supports direct code execution. R is a programming language used for statistical computing, while RStudio uses the R language to develop statistical programs. In R, you can write a program and run the code independently of any other computer program. R provides a variety of statistical methods (linear and nonlinear modelling, classical statistical tests, time series analysis, and classification) and graphical techniques and is highly extensible (Gelsey et al. 2022). Models appear as noisy clouds of points, whereas laws seem as continuous sequences of data points. As a result, formulating a model from data is far more difficult than the reverse engineering law. How do we choose which model best fits the data? Inverse probability, also known as likelihood, can be used to identify the model most likely to have produced the data. This allows us to fit many different types of models: linear, linear discrete, linear multivariate, linear multivariate with interaction terms, generalized linear models, and nonlinear generalized additive models. The model fitting algorithm for optimization is used. Each of the aforementioned techniques is tested in fitting the model. Finally, the algorithm uses the best model to fit the data.

The arithmetic means, standard deviations, and coefficients of variation were estimated monthly and annually for different climate factors, and the annual and monthly precipitation series for all stations for the available data.

Analysis of trends (increase or decrease) for all independent weather variables (e.g., rainfall, monthly, annual) was statistically examined in two phases. First, the Mann–Kendall (M-K) test (the increasing or decreasing trend is tested based on the value of the normative test) is used. In the second stage, the rate of increase or decrease in the trend was estimated using a slope estimator (Ifeka & Akinbobola 2015). Trend analysis was performed to detect the presence of upward and downward trends in the monthly and annual precipitation series using the M-K test:

The data values were evaluated as ordered time series. The following procedure was carried out for the M-K method analysis (Mondal et al. 2012).

• 1.

  Arrange data as ordered time series.

• 2.

  Let represent the first data point, i.e., ⁠, at time k and ⁠, ⁠,… ⁠, represent n data points at ⁠.

• 3.

  Compare the first-year data point. Let x, with ⁠, ⁠, ……_, i.e., year data point.

• 4.

  Assign values to the available data point as per the M-K equation.

• 5.

  Count the total number of positive and negative data points that occurred in the time series data which is termed as ⁠.

• 6.

  Identify how many sets of continuous +1 or −1 values occurred in the data series and were termed as tied groups.

• 7.

  n is the total number of years in the data series.

The presence of a statistically significant trend was evaluated using the Z value. A positive/negative value of Z indicates an upward/downward trend. In the present study, at a confidence level of 99, 95, and 90%, the positive or negative trends are determined by the test statistic. At the 99% significance level, the null hypothesis of no trend is rejected if > 2.575; at the 95% significance level, the null hypothesis of no trend is rejected if > 1.96; and at the 90% significance level, the null hypothesis of no trend is rejected if > 1.645 (Mondal et al. 2012).

To compare any two datasets, statistical equations are used. Through this study, the coefficient of determination (R²) method of comparison was used to evaluate the model.

The standard precipitation index (SPI) is a drought index that is based solely on rainfall in a given area. It depends on the probability of precipitation for any timescale. Some processes are rapidly affected by the behaviour of the atmosphere. The SPI was formulated by Tom Mckee, Nolan Doesken, and John Kleist at the Colorado Climate Center in 1993 (McKee et al. 1993). The 3-month SPI reflects short- and medium-term moisture conditions and provides a seasonal estimate of precipitation. The 6- and 9-month precipitation index indicates medium-term trends in precipitation. The 12-month SPI is a comparison of precipitation for 12 consecutive months with the same 12 consecutive months over all previous years for the available data. The SPI on these timescales reflects long-term precipitation patterns (MM Rasheed 2010).

Standardized precipitation evapotranspiration index (SPEI) is also used as a drought index, but it also includes a temperature component, allowing the index to calculate the effect of temperature on drought development by calculating the base water balance. The SPEI is an ideal indicator of the impact of climate change as temperature increases on drought (Vicente-Serrano et al. 2010).

Correlations between discharge and meteorological factors were examined on a monthly and seasonal basis. The relationships between discharge and air temperature as well as soil moisture, evaporation, precipitation, wind speed, and other factors were determined. This relationship was explained for each of the three study areas.

Hydrological models have a wide range of applications in water resource planning and management as well as flood forecasting and climate impact assessments. In the latter case, they are usually combined with meteorological or climate models. In this study, hydrological models were developed for the Atbara catchment to study the impact of climate change. The statistically developed models were calibrated and validated using the measured hydrological data.

In this study, the most common variables in climate change were studied to assess the severity of climate change in the river basin. Then a simple model was made based on the study of these factors to determine the extent of their impact on the river's discharge. Therefore, the rainfall trend and other climatic factors were estimated at various stations on the Atbara River. The result of each method is discussed in the following sections.

The site affects the climate of the Atbara River, as the Atbara River extends between latitudes 11° 40′ North and 9° 05′ North. Therefore, it extends across multiple climatic regions.

Table 2 shows the average maximum temperatures for the Upper Atbara and Setit region where the maximum is 39.68 °C in April and the minimum is 30.98 °C in August and the highest deviation is observed in February (1.87) and the lowest level in April (1.05) with a coefficient of variation 5.21 and 2.65%, respectively. It is also noted from the annual results that the average maximum temperature is 35.75 °C, corresponding to a deviation of 0.80 and a coefficient of variation of 2.23%. The non-standard M-K trend test was applied, and the results are presented in Table 2. Annual and monthly maximum temperature trends were obtained over the Upper Atbara and Setit area using the M-K test. The results showed that the annual and monthly maximum temperatures showed an increasing trend within the 99% confidence level, except for January, and no trend appeared within the studied significance level. The test also showed that the annual maximum temperature data have an increasing trend within the 99% confidence level.

Table S1 shows the average maximum temperatures for the Khashm el-Girba reservoir region where the average maximum temperature is 37.26 °C. The test also showed that the annual maximum temperature data have an increasing trend within the 99% confidence level. The non-standard M-K trend test for the Atbara Kilo 3 area showed that the annual and monthly maximum temperatures showed an increasing trend within the 99% confidence level and 95% confidence level, as shown in Table S2.

Table S3 shows the statistics of the average minimum temperatures for the Upper Atbara and Setit regions. The annual and monthly minimum temperatures showed an increasing trend within the 99% confidence level and 95% confidence level in January. The test also showed that the annual minimum temperature data have an increasing trend within the 99% confidence level. The same increasing trend was found in Khashm el-Girba and Atbara Kilo 3 regions as shown in Tables S4 and S5.

The Atbara River is seasonal. There is no rain during January, February, and December. The average annual precipitation is 503.76 mm, with a standard deviation of 97.80 and a coefficient of variation of 19.41%. Table S6 shows the average annual and monthly precipitation for the Upper Atbara and Setit region where the maximum is 172.97 mm in August and the minimum is 0.95 mm in November and the highest deviation is observed in August (52.62) and the lowest level in April (1.05) with a coefficient of variation of 30.42 and 0.97%, respectively. The annual and monthly precipitation did not show any trend within the studied significance level. The test also showed that the annual metrological data have no trend. Khashm el-Girba has no rain during the months of January, February, March, and December. The annual average precipitation is 394.22 mm. The maximum precipitation for the Khashm el-Girba region is 142.60 mm in August and the minimum is 0.59 mm in November. The annual and monthly precipitation did not show any trend within the studied significance level, except for June, which has a decreasing trend within the 95% confidence level, as presented in Table S7. The maximum monthly precipitation for the Atbara Kilo 3 region is 24.22 mm in August and the minimum is 1.00 mm in June, and the highest standard deviation is observed in August (21.51) and the lowest level in June (1.84) with a coefficient of variation of 88.80 and 184.04%, respectively. It is also noted from the annual results that the average precipitation is 46.76 mm, corresponding to a deviation of 31.17 and a coefficient of variation of 66.66%. The annual and monthly rainfall did not show any trend within the studied significance level, except for June and July, which has a decreasing trend within the 95% confidence level. The test also showed that the annual metrological data have no trend, as shown in Table S8.

The Atbara River region is characterized by the presence of southwest winds, which increase rain rates, especially in the summer months (Gebremicael et al. 2017).

The analysis showed an increasing trend of wind speed in the Upper Atbara and Setit, Khashm el-Girba, and Atbara Kilo 3 regions in almost all months as presented in Tables S9, S10, and S11, respectively.

Tables S12, S13, and S14 show that the annual and monthly runoff had no trend throughout the months of the year for Upper Atbara and Setit, Khashm el-Girba, and Atbara Kilo 3 regions, respectively.

Table S15 shows the average monthly solar radiation for the Upper Atbara and Setit regions where the maximum is 289.11 W/m² in April and the minimum is 222.30 W/m² in December and the highest deviation is observed in July (23.75) and the lowest level in November (4.90) with a coefficient of variation of 9.14 and 2.08%, respectively. It is also noted from the annual results that the average runoff is 256.74 W/m², corresponding to a standard deviation of 7.63 and a coefficient of variation of 2.97%. The annual and monthly solar radiation had a trend within the studied confidence level by 95% in May and by 99% in January, February, March, June, July, August, and September. It also indicates that there was no trend in October, November, and December. The test also showed that the data on annual solar radiation has an increasing trend within the 99% confidence level. The maximum monthly solar radiation for the Khashm el-Girba region is 289.96 W/m² in April and the minimum is 218.75 W/m² in December, and the highest standard deviation is observed in July (24.69) and the lowest level in November (4.56) with a coefficient of variation of 9.51 and 1.95%, respectively. The annual and monthly solar radiation had a trend within the studied confidence level of 95% in May and February, and 99% in January, March, June, July, August, and September. It also indicates that there is no trend in April, October, November, and December. The test also showed that the data on annual solar radiation have an increasing trend within the 99% confidence level as presented in Table S16. The maximum monthly solar radiation for the Atbara Kilo 3 region is 289.80 W/m² in May and the minimum is 202.38 W/m² in December. The results also showed that the annual and monthly solar radiation had a trend within the studied confidence level by 95% in September and October and by 99% in January, February, March, June, and July. It also indicates that there is no trend in April, May, November, and December. The test also showed that the data on annual solar radiation have an increasing trend within the 99% confidence level as shown in Table S17.

Tables S18, S19, and S20 show an increasing trend in almost all the months in the Upper Atbara and Setit, Khashm el-Girba, and Atbara Kilo 3 regions, respectively.

The analysis showed no trend of actual evapotranspiration in the Upper Atbara and Setit, Khashm el-Girba, and Atbara Kilo 3 regions in almost all months as presented in Tables S21, S22, and S23, respectively.

Table S24 shows the average river discharge for the Upper Atbara and Setit dam where the maximum is 5,758.22 MCM in August and the minimum is 175 MCM in December and the highest standard deviation is observed in August (2,843.21) and the lowest level in January (55.72) with a coefficient of variation of 49.38 and 27.70%, respectively. It is also noted from the annual results that the average hydrological data are 17,934 MCM, corresponding to a standard deviation of 3,710.10 and a coefficient of variation of 20.69%. The annual and monthly river discharge showed an increasing trend only during the month of May within the 95% confidence level, and there is no trend during the rest of the months. The test also showed that the annual hydrological data have an increasing trend within the 95% confidence level. This means that the hydrology of the river had no change during the studied time span. Table S25 shows the maximum river discharge for the Khashm el-Girba dam (5,365.74 MCM) in August and the minimum (25.7 MCM) in January. The average annual river discharge is 11,184 MCM, with a coefficient of variation of 42.83%. The annual and monthly river discharge showed an upward trend only during March, April, and May within the 99% confidence level and the 95% confidence level in February, September, and November. It was also noted that there was no trend annually in January, July, August, and December. The river discharge at Atbara Kilo 3 gauging station is a maximum of 5,140.66 MCM in August and a minimum is 10.71 MCM in February with a coefficient of variation of 39.88 and 383.28%, respectively. It is also noted from the annual results that the average hydrological data are 11,010 MCM, with a coefficient of variation of 39.08%. Using the M-K test, the results showed that the annual and monthly river discharge showed an upward trend only during the months of the year within a confidence level of 99%, except for January and February, where there is no trend. The test also showed that the annual hydrological data have an increasing trend.

The study found that there was no significant change in the precipitation over the basin, while there was a projected increase in temperature, wind speed, and solar radiation. This result is opposite to the results of Tariku & Gan (2018), which found an increase in precipitation in the basin.

The drought phenomenon in the study area was studied at the three stations using the default model for data analysis (SPI).

SPI3 had a maximum value of 2.46 in 1991, extremely wet. The lowest value was −3.72 in 1990, extremely dry. SPI6 had a maximum value of 2.41 in 1968, which expresses the intensity of a very humid climate (extremely wet). The lowest value was −3.88 in 1990, which reflects the extent of drought (extremely dry). SPI9 has a maximum value of 2.48 in 1968. The lowest value was −3.84 in 1990. SPI12 had a maximum value of 1.92 in 2003 (severely wet). The lowest value was −3.51 in 1990 (extremely dry). As shown in Figure S1, the values of SPI3, SPI6, SPI9, and SPI12 for the Khashm el-Girba region range from −3.84 to 2.48.

Figure S2 shows the values of SPI3, SPI6, SPI9, and SPI12, for the Atbara Kilo 3 region. The maximum value of all SPI ranges is 2.45 in 1989 for SPI3, expressing extremely wet. The lowest value was −3.08 in 1990 (extremely dry) for SPI12.

The SPEI is a simple multiscalar drought index that combines precipitation and temperature data. The SPI is calculated using monthly precipitation as the input data. The SPEI uses the monthly difference between precipitation and potential evapo-transpiration (PET). This represents a simple climatic water balance (Thornthwaite 1948).

SPEI3 had a maximum value of 2.34 in 1968, which expresses a very humid climate. The lowest value was −2.52 in 2016, which reflects the extent of the drought. The maximum SPEI6 was 2.84 in 1968, and the lowest value was −2.33 in 2017. SPEI9 had a maximum value of 2.59 in 1968. The lowest value was −2.01 in 1991. The maximum SPEI12 was 2.22 in 1968, and the minimum was −1.95 in 2017, as presented in Figure S3.

Figure S4 shows the values of SPEI3, SPEI6, SPEI9, and SPEI12, for the Khashm el-Girba region. The first 25 years are wet, but the rest are dry. This may be attributed to climate change.

Figure S5 shows the values of SPI3, SPI6, SPI9, and SPI12, for the Atbara Kilo 3 region. The maximum value of all SPI ranges is 2.22 in 1968 for SPI6 and SPEI12, expressing extremely wet. The lowest value was −2.45 in 2016 (extremely dry) for SPEI3. The values of SPEI3, SPEI6, SPEI9, and SPEI12 shows that at the Atbara Kilo 3 region the wet period was in the first 20 years, while the rest of the study period was dry. It is noticed that this region is opposite to the previous two areas in terms of drought. This may be explained by the relative difference between them in latitude.

Climatic factors affect the sources and distribution of rain and snow around the world. This can change river flows and rates of replenishment of aquifers (El-Mahdy 2022). Precipitation and snowfall are largely attributed to global climatic conditions. The hydrogen and oxygen isotopes of precipitation are highly sensitive indicators of their sources and history in the water cycle and are fundamental to our understanding of many environmental processes. In this context, the study reviewed some of the impact of climatic factors on the different stations of the Atbara River such as precipitation, high and low temperatures, evaporation rates, and solar radiation on hydrology.

It is evident in Figures S6, S7, and S8 that there is a direct relationship between precipitation, runoff, and actual evapo-transpiration (ET) with river discharges for the Upper Atbara and Setit regions.

The minimum temperatures in the Khashm el-Girba area range between 13.5 and 27 °C. The minimum temperatures rise as much as possible in June, July, August, September, and October, and begin to decline in the remaining months of the year. During periods that reach a minimum temperature, the discharge rate is also high. This means that the relationship between the two variables is a direct relationship, as presented in Figure S9. The actual ET process in the Khashm el-Girba area is absent in the first months of the year and also in the last months of the year. It reaches its maximum value in the months of the flood and ranges between 0 and 180 mm during the period from 1975 to 2020. It is clear from Figure S10 that the relationship between the discharge and the actual ET is a direct relationship. The area of Khashm el-Girba precipitation ranges between 0 and 277 mm. In the months of the flood, the values of precipitation are large, and the rest of the months of the year are non-existent. It is clear from Figure S11 that the relationship between the precipitation in the area and the value of rainfall is directly correlated.

Figures S12, S13, S14, S15, and S16 show inverse correlations between the discharge and maximum temperature, minimum temperature, shortwave radiation, Ref ET, and actual ET, respectively. Figures S17 and S18 show direct correlations between the discharge and precipitation, and runoff, respectively. Temperature and evaporation parameters increase water losses leading to fewer discharges. On the other hand, precipitation increase may lead to an increase in water runoff and discharge (El-Mahdy et al. 2021).

First, all climatic elements such as maximum and minimum temperatures, wind speed, solar radiation, soil moisture, precipitation, and other climatic factors and their relationship to the discharges of the three stations on the Atbara River were studied. Then, modelling of these data was done using the RStudio program to develop a relationship between the discharge and the climatic variables, and the following was found.

The optimized model constants found were as follows:

In Figure S19, the extent of concordance between the results of the model and the actual discharge of the Upper Atbara and State reservoirs in the years from 2016 to 2020 is shown. The developed model is not quite suitable. Another trial may be beneficial.

The parameters of the model are as follows:

In Figure S20, the extent of dispersion between the results of the model and the actual discharge of the Khashm el-Girba reservoir, specifically the period from 2011 to 2020, the period in which the upper Atbara and Setit reservoirs were established, which necessitated a separate study of the case of the Khashm el-Girba reservoir in this period in a separate way. So another trial is necessary.

The kilo 3 trial factors are as follows:

It is obvious from Figure S21 that the developed model quality is bad, since the variation between the results of the model and the actual discharge of the Atbara Kilo 3 station is high. This also means that there is a direct effect of the discharges of the upper Atbara and Stet reservoirs on the discharge of the Atbara Kilo 3 station in addition to the presence of climatic elements that increase the degree of dispersion.

The time series of the flow of the Atbara River has been statistically studied. Simulations are used as input to the projected water resource management system (Hao et al. 2015) when statistically studying the hydrological data of the Atbara River. It was found that there is a difference in the flow of the river before and after the construction of the Upper Atbara and Setite reservoirs. So two models were made – the first before the construction of the reservoirs and the other after construction. Therefore, the prediction of the discharges at the three stations depends on the post-construction model.

The factors of the accepted model are as follows:

A discharge prediction model for the Atbara River was built using RStudio software using an analysis of the factors affecting the hydrology and water resources of the Atbara River (precipitation, temperature, wind speed, relative humidity, and radiation) and their relationship to the behaviour of the Atbara River. Future discharge predictions at these stations were extracted from the model using projected climate data from CORDEX RCMs with two emissions scenarios: the RCP 4.5 scenario and the RCP 8.5 scenario. A trend analysis was performed to ascertain the effects of climate change on the river. Trend analysis showed that the predicted climatological parameters are very close to their historical records. Atbara River modelling is a simplified representation of the river system, and its evolution was developed successfully after many trials. According to the expected climatic data, a slight increase in the discharge of the Atbara River can be expected. It was noticed that the maximum expected values of discharge at the upper Atbara and Setit are 18,722 BCM in 2025 and the lowest expected value is 10,174 BCM in 2032 using RCP 4.5 scenario. However, using RCP 8.5 scenario, the maximum expected values of discharge at the upper Atbara and Setit are 19,844 BCM in 2046 and the lowest expected value is 11,938 BCM in 2034. The average predicted discharge of the river in both scenarios is larger than the historical records. It was noticed that the maximum expected value of discharge at the Khashm el-Girba is 27,336 BCM in 2025 and the lowest expected value is 6,388 BCM in 2032 using RCP 4.5 scenario, but using RCP 8.5 scenario, the maximum expected values of discharge at the Khashm el-Girba is 35,923 BCM in 2024 and the lowest expected value is 9,303 BCM in 2048. The maximum expected value of discharge at the Atbara Kilo 3 station is 27,098 BCM in 2048 and the lowest expected value is 9,732 BCM in 2032 using RCP 4.5 scenario. Using RCP 8.5 scenario, the maximum expected values of discharge at the Atbara Kilo 3 station is 30,433 BCM in 2025 and the lowest expected value is 9,529 BCM in 2022. The climate change impact on Atbara River discharge may be a slight negative. Modelling the Atbara River can allow us to solve some problems and thus provide a complementary way to configure theory about the history of the river and its stages of development. More studies on the discharges of the Atbara River at other points, with some modifications, will be useful to estimate the best discharge of the river. Taking into account the inflows and outflows from the river will give us a future picture of the river balance. Conducting several field measurements of the Atbara River in several distinct locations to know the changes in the discharges may enhance the model. The Atbara River model can be developed to estimate river discharge for different time steps such as daily, seasonal, or annual, which will certainly be useful for planning and managing water resources projects for related time steps.

Conceptualization: E-M.M.E-S. and M.M.; methodology: E-M.M.E-S., S.M.A., M.M., and A-E.S.; software: E-M.M.E-S. and M.M.; validation: E-M.M.E-S. and M.M.; formal analysis: E-M.M.E-S. and M.M; investigation:, E-M.M.E-S. and M.M; resources: E-M.M.E-S., S.M.A., M.M., and A-E.S.; data curation: E-M.M.E-S. and M.M; writing – original draft preparation: E-M.M.E-S. and M.M; writing – review and editing: E-M.M.E-S., S.M.A., M.M., and A-E.S.; visualization: E-M.M.E-S. and M.M; supervision: E-M.M.E-S. and M.M; project administration: E-M.M.E-S. and M.M. All authors have read and agreed to the published version of the manuscript.

This research received no external funding.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.