The influence of gravity waves on the climate change over upper Blue Nile basin in Ethiopia

Precipitation and temperature are the most fundamental meteorological/weather parameters with high spatiotemporal variability over any region of the Globe. Over Ethiopia, Upper Blue Nile basin (UBNB) is the major water resources for irrigation and societal needs not only for Ethiopia but also for downstream countries. However, the exact mechanism to study climate change is not yet satisfactory. Climate variability over UBNB is too high due to its variable topographical features. Gravity wave is one of the most influencing factors to climate change. However, there is no study conducted by considering gravity wave activities on the effect of climate change over UBNB. Therefore, the attempt is made the influence of gravity waves on climate change and variability over UBNB. To this end, we inferred different data sources (reanalysis and ground based). Kinetic energy and momentum equations were used in this study. The results indicate that the reanalysis (ECMWF) precipitation and temperature data were well agreed to the ground based data with correlation coefficient of 0.83 and 0.41 respectively. Strong gravity wave takes tropospheric cloud to stratosphere which causes drought events, while weak gravity wave moves lower tropospheric cloud to tropopause which leads to the occurrence floods. Generally, gravity wave activities affected precipitation and temperature distribution during rainy season. Hence, future study is quite useful to investigate the frequency of high gravity wave occurrence in connection to Ethiopian drought events.


Introduction
The climate of Upper Blue Nile Basin (UBNB) is classified as tropical climate with high humidity, a considerable amount of sun, abundant rainfall and temperatures that are extremely variable throughout the year (Abera et al. 2017;Megbar et al. 2019). The basin is quite useful for agricultural due to availability of ground and surface water (Megbar et al. 2018(Megbar et al. , 2019. A good understanding of rainfall variability is essential for long-term hydrological and climatological studies and applications, as an input for models of crop growth, design of urban drainage system and land management systems (Suhaila & Jemain 2009;Ho et al. 2013). Heavy rainfall could also cause floods and landslides that may affect the agricultural products (Conway 2000;Ayehu et al. 2018;Dinku et al. 2018). The shortage of rainfall could also lead to scarcity of water and has an adverse impact on agricultural yield that brings the problem of economic activities (Mahmudul et al. 2012). Farmers over UBNB are follows rain feed agriculture to balance energy and food security. However, precipitation over UBNB has high spatiotemporal variability due to known and unknown factors. Different researchers indicated that, in recent years gravity wave is one of the factors that affect precipitation and temperature distribution (AttaullahKhan and ShuanggenJin 2016; Megbar et al. 2019).
Gravity wave and space weather are very dynamical variable features of the atmosphere and that influenced not only clouds and temperature but also precipitation and crop production (Jensen et al. 2010;Dinh et al. 2016;Lars et al. 2016;Jensen et al. 2016;Aurélien et al. 2017, Megbar et al. 2019). The transport of tropospheric cloud to stratosphere (leads to drought) is one of the gravity wave effects (Megbar et al. 2019). Gravity waves are moves ozone concentration from stratosphere to troposphere (increase the surface temperature of the Earth) (Satomura and Sato 1999;Sato 2000;Vadas et al. 2003;Aurélien et al. 2017). High frequency gravity waves are influenced the cooling rates of air parcels in the atmosphere (e.g., Lindzen 1981;Jensen et al. 2016). The formation of the cold polar summer is the means of energy and momentum transportation from the lower atmosphere to the middle atmosphere by gravity waves (e.g., Lindzen 1981). It influenced the environmental flow through wave drag and dispersion. The amount of momentum is transported by gravity waves; it depends on the precipitation flux (AttaullahKhan and ShuanggenJin 2016). This paper may not be to give strong attention only the impact of gravity wave, but also assessing the influence of Sunspot on climate change. Solar variations cause change space weather and to some degree weather and climate on Earth. The feature of solar variability is fluctuations of plasma in the Sun-Earth space environment. The influence of solar variability on climate system has been a controversial subject from a long time.
Models typically use only simplified linear parameterization schemes of precipitation, temperature and gravity wave drag, resulting in larger discrepancies between model and measurement data (e.g., Kathrin et al. 2018). Therefore, additional data are required for validation and more direct observation data are necessary for improving the parameters (Geller et al. 2013). There are approaches of gravity wave parameterization schemes, which improve the structure and magnitude of tides, but a validation with observational data is still rare (Yigit and Medvedev 2017;Kathrin et al. 2018). Especially, over UBNB was not made a validation due to lack of instrumentation and skillful person. In this study, the validations were done on the data of ECMWF precipitation and temperature against in-situ measurement for sure impacts of gravity wave on the climates over the study area.
Recently, impact of gravity waves and space weather in climate change were studied by Jensen et al. (2016) in tropical region, Lars et al. (2016) in Polar Regions and Aurélien et al. (2017) in Hertzog. A wide range of scholars studied about precipitation variability over UBNB. Example, (Bewket 2010;Ayalew et al. 2012;Mekonnen et al. 2014;Yitea and Medvedev 2015;Gizachew and Yihenew 2015;Takele et al. 2017). Our research is also the first in its kind on impact of gravity waves on temperature and precipitation variability in Ethiopia as well as UBNB. This research has demonstrated the impact of gravity waves on temperature and precipitation variability over the basin.

Study area description
UBNB in Ethiopia is located between 7.4 0 to 12.5 0 Latitude and from 34.25 0 to 39.49 0 Longitude ( Fig. 1) with a drainage area of about 176, 000 km 2 . The basin's climate varies from humid to semiarid (Abera et al. 2017). The annual precipitation increases from northeast to southwest (Mariam et al. 2016) opposite distribution with temperature. Specifically, its hydrological behavior is characterized by high spatiotemporal variability (Conway 2000;Abera et al. 2017).
Since UBNB has the share of the total Nile flow, it is the economic mainstay of downstream countries (i.e. Sudan and Egypt) (Dagnenet Fenta 2016; Abera et al. 2017). The topography of UBNB is very complex, with elevation ranging from 500 m in the lowlands with high temperature at the Sudan border to 4160 m in the upper parts with low temperature of the basin (Conway 2000;Abera et al. 2017;Megbar et al. 2019). Due to the topographic variations, the climate of the basin varies from cold to hot, with large variations in a limited elevation range (Megbar et al. 2019). The mean annual rainfall of the UBNB are estimated to be in the ranges of 950 to1600 mm (Conway 2000;Megbar et al. 2019)

ECMWF reanalysis data
ECMWF reanalysis dataset (ERA-Interim) is unique from other datasets because it has different data types. Precipitation, temperature, cloud cover, kinetic energy of the atmosphere and gravity wave data were obtained from 1979 -2018 from ECMWF model. The data are available in (https://cds.climate.copernicus.eu) or (www.ecmwfdataset) (Kallberg et al. 2004;Berrisford et al. 2011aBerrisford et al. , 2011bDee et al. 2011). The derived ECMWF products are used for making the crosscomparison to the co-located observations and diagnose the variability of precipitation and temperature at daily time scale over the study domain. The current updating grid horizontal resolution is 0.125 × 0.125 degree (Megbar et al. 2019). ERA-Interim is based on an atmospheric model and reanalysis system with 60 pressure levels in the vertical with a top level at 0.1mb (Berrisford et al. 2011b). Furthermore, the Sunspot data was obtained from NASA from different satellite observation.

Methodology
The study has been conducted numerically and analysis of the output from the model is made by the help of MATLAB software.
The potential energy (E p ) of the gravity wave can be calculated as where g is gravitational acceleration, N is peck frequency, T is time series temperature obtain from the model, T  is perturbation temperature and T is average temperature.
The total energy of gravity waves is where k E and p E are kinetic and potential energy of gravity waves respectively.
We have also assessed the correlations among different parameters to characterize negative, positive and zero correlations. The correlation coefficient of climate variability were calculated Where, R is correlation coefficient, X is representing climate parameters, Y is representing gravity wave; X and Y bar are the mean value of the data. To characterize the future climate and impact of gravity wave activity, the trend analysis was calculated.

Results and Discution
High temperature, precipitation, cloud cover and gravity waves on the UBNB surface triggers deep convective mixing in the lower troposphere was calculated. The calculated temperature and precipitation from ECMWF model showed good correlation to in-situ measurements as we can see in Fig.2. The gravity wave activities are enhanced during the spring season over the UBNB that lead to decrease the temperature and water vapor to defuse in to the stratosphere as shown in Figs.4 and 5. When gravity waves propagate and break, it transports not only energy and momentum, but also deposits vertical mixing of heat and affects temperature directly or indirectly as shown in bottom left and right panel of Fig.3. If the time series is shortened, the cutoff period is smaller as well and the spectral response for long-period waves was reduced even further. Strictly speaking, this implies that gravity wave analyses of time series to compare with precipitation, temperature space weather, and cloud cover was investigated in Figs.6 and 7.
For comparison the same analysis was done for temperature deviations induced by gravity waves (Ehard et al. 2015;AttaullahKhan and ShuanggenJin 2016). The calculated trend analyses of atmospheric parameters for the same altitudes were observed in Fig.7 for the temporally filtered data.

Comparisions of ECMWF data against the ground based
Comparison of ECMWF data against the ground truth /in-situ data/ has been made in Fig. 2.

Fig.2
Variation in precipitation around the basin was found to be periodic (Fig.2, a). It follows the same pattern almost with in every 5years. The plot also shows that the time series variation in precipitation is nearly the same between in-situ measurements and ECMWF data ( (Fig.2, b).
Temperature variation is relatively smooth as compared to precipitation variability. The variation in temperature is also somewhat periodic. Time variation of temperature from ECMWF data and in-situ measurements are following the same pattern.
As we can see from Fig. 2 in part 'a', the red and the magenta lines assigned to in-situ and ECMWF reanalysis temperature data, respectively, while the red stars and the black smoothed lines in Fig.2 in part 'b' indicates the error deviation between temperature from in-situ and ECMWF, respectively. From 1981 to 2017, ECMWF temperature data were varied from 18.0 to 19.7 °C with an average of 18.8 °C, while in-situ was varied from 18.5 to 21.5 °C with an average of 19.9 °C. The range of the deviation which calculated from in-situ measurement mines ECMWF temperature data were varied from 0.5 to 3.0 °C with an average of 1.5 °C. Whereas, precipitation from in-situ observation was varied from 3.0 to 4.3 mm per day with an average of 3.5 mm per day, while from ECMWF products varied from 2.9 to 4.2 mm per day with an average of 3.47 mm per day, we can see from Fig. 2 in panel 'c'. Hence, the errors were calculated from gauge observation mines ECMWF precipitation products which varied from − 0.1 to 0.5 mm with an average of 0.1 mm. Further explanation of the error metrics is provided in Table 1. The correlation coefficient of ECMWF and in-situ temperature, and precipitation data were found to be 0.32 and 0.82, respectively. The bias ratio, MRE, and RMSE between in-situ and ECMWF temperature data were found 0.81, -0.10, and 3.82, respectively, while with precipitation data were 0.98, − 0.01, and 0.71, respectively, we can see in Table 1. Precipitation products from ECMWF were well agreed with in-situ observations, whereas the magnitude of insitu temperature data was slightly greater than ECMWF reanalysis data. After estimated the error deviation, ECMWF data are widely used to supplement the sparse density and irregular distributions of in-situ data over UBNB. This kind of validation was studded by Megbar et al.

The global and the Ethiopia annual climate elements spatial distribution and relations among them
Spatial distribution of climate elements and their relations in the global and Ethiopia context have been demonstrated in Fig.3.

Fig.3
The global precipitation distribution and cloud clover were observed in the top left and right panel of Fig.3 respectively. In the cause of the western part of African continents the amount of precipitation is high with compared to the rest. Owing to this, the eastern part of the Africa, especially Ethiopian highlands the precipitation distribution is high due to its complex topography features (see in Fig.3). From the seven Continents, South America and Africa have been light annual precipitation observed. Similar distribution of cloud cover over the globe like that of precipitation was indicated the top right panel of Fig.3. The global temperature distribution is observed bottom left panel of Fig.3, where as gravity wave is provided in bottom right panel of Fig.3. The effect of gravity wave on the climate system of the glob was severed in the continents than the ocean. Coming to African continent, especially over Ethiopian highlands the gravity wave distribution is high with compared to the rest parts. The correlation between strong gravity wave and precipitation distribution is negative as shown in eastern and east north part of Africa and middle Europe. Moderate and weak gravity wave was positively correlated with precipitation. Coming to Ethiopian, especially over upper Blue Nile basin (UBNB) moderate gravity wave and precipitation positively correlated with correlation coefficient of 0.81; while strong gravity wave and precipitation negatively correlated with the correlation coefficient of -0.62. The seasonal variation of precipitation due to temperature, cloud cover, and gravity wave were provided in Fig.4 and 5. Different researchers such as Ehard et al. (2015) indicated that gravity wave has impacts on temperature distribution but not attention on precipitation distribution. This paper is unique from the previous researchers finding owing to strong and weak gravity wave impacts on cloud and precipitation in addition to temperature as shown in Figs.3, 4 and 5.

The spatiotemporal variability of climate elements over UBNB in Ethiopia
Spatial and temporal variability of climate elements and their seasonal variation over UBNB is provided in Fig.4.

Fig.4
Moderate gravity wave around the central part of Chokie Mountain is responsible to transport cloud to the dew point for condensation during summer season. It is because of this reason that the central part of UBNB around Chokie Mountain area is rich in precipitation. The cloud cover is less in the north eastern part of the basin. This is because the gravity wave was very high and takes the moisture from the troposphere to the stratosphere before it gets freeze as indicated in the bottom right panel of Fig. 4.

The temporal variability of climate elements and their relations
Time variation of climate elements with their relation was demonstrated in Fig.6.  Table 2 Low gravity wave was found between 17000 and 22000 J/m 2 , while moderate gravity wave was found in the range of 22000≤ Gravity wave value<24000 J/m 2 , whereas strong gravity wave was found the value greater than 24000 J/m 2 . After 2005, the trend of precipitation was negative except some years as shown in Fig.7. Very negative trend was observed the year between 2014 and 2015. In these years in Ethiopian history severe drought events were happened due to El-Nino occurrence as suggested by Kelem and Derbew (2017) Fig.7. During those years, in Ethiopian history severe drought was observed (Megbar and Tadese, 2018). The occurrence of the 1992 drought was associated with the creation of strong Sunspot number, while in 2002 drought occurrence was due to the strong gravity wave presence, whereas in 2013 associated with the combined effect of strong gravity wave and Sunspot number as provided in Fig.7.

Table 3
Temperature was positively correlated to Sunspot number while it has negative correlations with gravity wave. Hence gravity wave has its own advantages to reduce the Earth`s temperature, while strong gravity wave has negative impact on precipitation. The 11 years solar cycle has negative impact on Earth`s climate system by increase the global temperature and too degrease the precipitation which leads drought as shown in Table 3.

Conclusions and recommendations
We evaluated the extent to which climate elements have been varying in the past 30 years and the influence that the elements have on each other. Emphasis has been give on the way how gravity wave influences the climate system of the UBNB. When the gravity wave is high enough it transports moisture from the troposphere to the stratosphere before condensation leads to scarcity of precipitation and consequently drought event were occurred. When the gravity wave is weak it is unable to transport moisture to the dew point for condensation. However, scarcity of precipitation may not be occurred. When the gravity wave is moderate to transport moisture from the lower troposphere to tropopause so that condensation is very possible and floods were occurred. Further study will need to determine the frequency of strong gravity waves occurrence and its relation to the Ethiopian drought events. In order to estimate exact amount of precipitation over study area, it needs consideration of atmospheric chemistry in addition to consideration of gravity wave and space weather effects.

Abbreviations
ECMWF: European Center of Medium Weather Forecast ENMA: Ethiopian National Meteorological Agency UBNB: Upper Blue Nile Basin R: Correlation Coefficient would like to thank people surrounding us for their substantial involvement on the research in one or the other way.

Authors' contributions
MW designed the computational simulations and analysis; furthermore he drafted the entire document. BA and TN were contributed to the analysis and drafting. They also contributed the physical atmospheric analysis. All authors read and approved the final manuscript.

Funding
This work was supported by Debre Markos University.

Availability of data and materials
Cloud cover, Precipitation, Temperature, and Gravity wave data were obtained from ECMWF model is freely available in www.ecmwfdataset and Ethiopian National Meteorology Agency.