Evaluation of Seven Gap-Filling Techniques for Daily Station-Based Rainfall Datasets in South Ethiopia

Africa Center of Excellence for Climate-SABC, Haramaya University, P.O. Box 138, Haramaya, Ethiopia Department of Environmental Science, Wolaita Sodo University, P.O. Box 138, Wolaita Sodo, Ethiopia Department of Crop Production, Faculty of Agriculture, University of Eswatini, P.O. M205, Luyengo, Eswatini Ethiopia Institute of Agricultural Research, Melkasa Research Center, P.O. Box. 436, Adama, Ethiopia Faculty of Meteorology and Hydrology, Arba Minch University, P.O. Box. 21, Arba Minch, Ethiopia


Introduction
Rainfall (precipitation) is one of the key inputs in many disciplines such as climatology (climate variability and change), meteorology (weather conditions), irrigation engineering (irrigation scheduling), hydrology (water cycle), and environmental hazard assessment (floods). Despite its overriding uses, the rainfall dataset of meteorological stations has gigantic missing values, mainly in developing countries [1][2][3]. Data gaps in rainfall time series are predominantly caused by the provisional absence of observers, equipment miscarriage, data archiving, and irregular calibration of devices [4,5]. Ignoring the missing values from analyses has been used as a technique to manage it [6][7][8]. However, it leads to partial (coarse resolution) and biased results in data analyses [9][10][11]. Instead, filling the data gaps using reference datasets such as reanalysis products or estimates from the surrounding stations are better and widely used approaches [12][13][14][15]. Ample gap-filling techniques have been evaluated and suggested in the literature to fill in the missing daily rainfall time series at different parts of the world. e majority of gap-filling techniques are spatial interpolation methods.
Among the spatial interpolation techniques, simple arithmetic mean (SAM) was indicated for its best performance and computational simplicity in some studies [16][17][18]. But, [19,20] prioritized inverse distance weighting (IDW) over other spatial interpolation techniques. Outperformance was also reported for the normal ratio method (NRM) [16,21,22], correlation coefficient weighing (CCW) [23], and multiple linear regression (MLR) [24]. Nevertheless, Longman et al. [25] specified no statistical differences (similar performance) between five spatial interpolation techniques (normal ratio method, linear regression, inverse distance weighting, quantile mapping, and single best estimator) for large gaps. Machine learning processes such as the artificial neural network (ANN), Kernel approaches, and kriging are also suggested in some studies to fill the rainfall data gaps. e best performance of the machine learning process was stated for ANN [26,27], ordinary kriging [28,29], and Kernel approaches [30]. Besides, Grillakis et al. [31] indicated the acceptable performance of empirical quantile mapping in filling the discontinued daily rainfall data in the Mediterranean island of Crete.
Combining or modifying the previously existing gapfilling techniques is also reported for better performance than using the techniques separately. Teegavarapu et al. [32] indicated that the linear weight optimization method (LWOM) with a single best estimator (SBE) performed better than SBE only in Florida. Similarly, Kim and Pachepsky [33] concluded that the regression tree (RT) with ANN showed better performance than solely using RT or ANN in the Chesapeake Bay watershed of the USA. Furthermore, Khosravi et al. [34] presented better performance of the modified geographical coordinate (GC) method than the previously available methods in 24 station gauges in Iran. Martínez et al. [35] also showed that the generalization of the modified normal ratio with the inverse distance weighting and the generalization of modified correlation coefficient with the inverse distance weighting method outperformed NRM, NRM weighted with correlation, NRM modified with IDW, CCW, modified CCW, IDW, modified correlation coefficient with IDW, IDW weighing of NRM with correlation, and IDW-modified height. Similarly, Rahman et al. [36] indicated that the generalized linear model with gamma and Fourier series was outperformed over SAM, NRM, CCW, and IDW in estimating the missing daily rainfall series. e Gaussian mixture model-based KNN imputation showed better performance level than KNN only [37].
Filling the rainfall data gaps using the reanalysis products is also another widely used approach. For example, Cordeiro and Blanco [38] indicated that the Climate Hazards Group InfraRed Precipitation with Stations (CHIRPS) product outperformed the tropical rainfall measuring mission (TRMM) and Morphing Technique (CMORPH-CPC) in estimating daily rainfall time series in the Amazon region. Further, Tang et al. [14,15] filled the data gaps in daily rainfall of North America (serially complete NA) and the globe (Serially Complete Earth) dataset using the global historical climatology network daily (GHCND), a global surface summary of the day (GSOD), and Environment and Climate Change Canada (ECCC). In addition, Noh and Ahn [39] developed a new gridded rainfall dataset (K-Hydra) over the Korean peninsula to fill rainfall data gaps, which has comparable performance with global precipitation climatology project (GPCP), climate prediction center (CPC), tropical rainfall measuring mission (TRMM), and Asian precipitation highly resolved observational data integration towards evaluation (APHRODITE).
In Ethiopia, some studies evaluated and suggested different gap-filling techniques for daily rainfall time series. For instance, Boke [40] evaluated five spatial gap-filling techniques in ten meteorological stations in Ethiopia and suggested the nearest neighbor, inverse distance weighting average, and modified inverse distance weighting average for the country. Woldesenbet et al. [41] also tested four gapfilling techniques in 38 stations in the upper Blue Nile basin of Ethiopia in which CCW showed the best performance over NRM, modified NRM, and IDW. Similarly, Armanuos et al. [17] assessed twenty-one (21) gap-filling methods in 15 stations and suggested that NRM, MLR, IDW, CCW, and SAM fill in the missing rainfall data in Ethiopia. e reviewed literature indicates that the performances of gapfilling techniques vary between stations, considered evaluation criteria, statistical properties of data [17], and density and the geometrical organization of the station network [42]. Yet, to the authors' best knowledge, none of the reviewed literature and no related study covered the meteorological stations located in Wolaita Zone and the surroundings. Moreover, the applicability of gap-filling methods is limited by many factors including the required computational skill and the percentage of gaps in the data [43]. On the other hand, Ethiopia is a large country covering about 1,104,300 square kilometers [44] in which directly using any of the suggested techniques for the entire country is not representative and can lead to biased results. So, testing the gapfilling techniques at local levels is very important. us, this study was initiated to evaluate the performances of seven gap-filling techniques to fill in the missing values of daily rainfall data in the meteorological stations of Wolaita Zone and the surroundings in South Ethiopia. e seven selected techniques were simple arithmetic mean (SAM), normal ratio method (NRM), inverse distance weighting (IDW), correlation coefficient weighing (CCW), multiple linear regression (MLR), empirical quantile mapping (EQM), and empirical quantile mapping plus (EQM + ). e techniques were preferred among others due to their computational simplicity, wider application, and comparable performance with other techniques [45]. Performances of the techniques were tested against four evaluation criteria such as mean absolute error (MAE), root mean square error (RMSE), skill score (SS), and Pearson's correlation coefficients. As well, the performance consistency was evaluated on different time scales. e authors of this paper expect momentous contributions of the paper to environmentalists, engineers, climatologists, agriculturalists, and natural resource 2 Advances in Meteorology management experts facing rainfall data gaps.
e techniques included in this study can be tracked on any other location and their performances can be compared with the findings of this work. Besides, the filled rainfall datasets of five meteorological stations (Areka, Bele, Boditi, Hosana, and Shone) are freely available based on requests. Moreover, our findings have a substantial contribution to sustainable development goal (SDG) thirteen (climate action) by providing the filled and summarized rainfall data freely so that the policymakers of the country can use it to understand the climate variability and change in the study area with reduced error level. So, it provides imperative information to take action on climate change adaptation and mitigation measures. e rest part of this paper is organized into four sections. Section 2 describes the materials and methods: study area and data description and methodology for gapfilling techniques and evaluation criteria. Section 3 presents the results of the gap-filling techniques of the missing daily precipitation data in five meteorological stations. Section 4 discusses and interprets the results. Finally, Section 5 concludes the findings of this study.

Study Area and Data
Description. Five meteorological stations located in two zones (Wolaita and Hadiya) of southern nations' nationalities and people's regional state of Ethiopia were included in this study (see Figure 1). From the five stations, two (Hosana and Shone) are located in Hadiya Zone and three stations (Areka, Bele, and Boditi) are located in Wolaita Zone. e five meteorological stations considered in this study are sufficient and comparable with the four stations [46,47] and six stations [48] of similar studies. e stations are located from 6.92 to 7.57°(latitude) and from 37.5 to 37.95°(longitude) and in the altitudinal ranges of 1240-2397 meters above sea level (see Table 1). e observed daily rainfall and maximum and minimum temperature data of five stations for periods  were obtained from the National Meteorological Agency (NMA) of Ethiopia [49]. e stations have huge missing values up to 30.2% in daily rainfall, 29.4% in maximum temperature, and 19.4% in minimum temperature (see Table 1). Besides, Bele and Shone stations did not have the dataset for maximum and minimum temperature in the study period. So, the two stations were not considered in analyses of maximum and minimum temperature (see Table 1). e rainfall datasets of five stations have a bimodal pattern (two peaks in the year) even though the months of obtaining peak values slightly vary from station to station (see Figure 2, presented in bar charts). Two peak values of rainfall were observed in April and August in Areka and Hosana stations, April and July in Shone, May and August in Boditi, and May and July in Bele stations. e study area received an annual rainfall between 1,212 (in Hosana) and 1,561 mm (in Shone). Besides, the maximum temperature has a bimodal distribution pattern (see Figure 2: presented in lines). e mean monthly maximum temperature varies between 19.34°C (in Hosana) and 29.5°C (in Areka) (see Table 1). e minimum temperature of the area has a continuously decreasing trend from February and March to December. It ranges between 8.65°C (in Hosana) and 15.4°C (in Areka) (see Table 1).

Methodology.
e methodology of this work trailed the following processing steps. First, the data matrixes of five stations with complete data (excluding the years of data missing) were prepared. For the gap-filling techniques other than quantile mapping and quantile mapping plus, the datasets of five (all) stations were considered. In the empirical quantile mapping (EQM and EQM + ), the datasets of three stations (one target and two with higher correlation coefficients) were used. e correlation between a target station and the surrounding stations is more important than proximity (physical distance) of the stations [25]. en, the seven gap-filling techniques were cross-validated using four evaluation criteria, and the missing values were estimated using the best-performed technique. In the case when there is no data from neighboring stations, the method used by Ismail and Ibrahim [50], using the mean on the same day and month but at different years, was used to estimate the missing value on that particular date. e detailed methodology is described in the following paragraphs.

Simple Arithmetic Mean (SAM).
It estimates the missing values in the target station from the surrounding stations by simply taking the average of surrounding stations' data in the same period of missing value [51]. is is the simplest technique of estimating missing values used when the missing value has less than 10% [52]. It is expressed as where V o is the estimated value of the missing data, V i is the value of the same variable at the i th nearest station, and n is the number of nearest weather stations considered for averaging.

Normal Ratio Method (NRM).
It considers the correlation coefficients between the target station and the surrounding stations. It is recommended for filling in missing values if more than 10% of the data is missing [52]. It gives weight to the data of surrounding stations based on their correlation with the target station. It is expressed as follows: where V o is the estimated value, W i depicts the weight of the i th surrounding weather station, and V i is the value of the same variable at the i th station. e weight of the surrounding station is calculated using the following equation: where W i is the weight of the i th station, r i corresponds to the correlation coefficient between the target station and the i th surrounding station, and n i is the number of points used to calculate the correlation coefficient.   [53]. It assumes that the closer the surrounding stations to the target station, the better the estimation of missing values and the lower the error in estimation or the better the accuracy. It is calculated using the following equation where V o is the estimate obtained for missing value, V i is the observed value at the i th station, d i is the i th surrounding station distance, and n is the number of stations used. e distance between the target station and the surrounding stations is calculated using the Pythagoras formula.
where d i is the distance between the target station and the surrounding i th station, X a and X i are the longitudes, and Y a  and Y i are the latitudes of the target and the i th surrounding stations, respectively. en, the values in degrees are multiplied by 111 to convert them to kilometers.

Correlation Coefficient Weighing (CCW).
In this approach, distance is replaced by Pearson's correlation coefficients [54]. It assures that the datasets of surrounding stations having a better positive correlation with that of the target station give better estimates of missing values in target stations than that of less correlated ones. us, Pearson's correlation coefficients between rainfall data of five meteorological stations were analyzed, and the missing values in target stations were determined using the following equation: where V o is the missing value of the target station, r i is the correlation coefficient of the i th surrounding station, and V i is the value of the same variable in the i th surrounding station.

Multiple Linear Regression (MLR)
. It was carried out by considering the linear significant relationship between the observed values of the target station and the surrounding stations [55]. e dataset of the target station was considered as a dependent variable and the surrounding stations' datasets were considered as independent variables. Accordingly, the multiple linear regressions were carried out for five stations. en, the missing values in the target station were filled using the intercept and the coefficients of the variables were expressed as follows: where V o is the estimated value, a 0 , a i , . . . , a n are regression coefficients, and V i is the value of the same parameter at the i th weather station.

Empirical Quantile Mapping (EQM).
It is a very common technique used to downscale the global circulation model (GCM) outputs of rainfall to the regional and local levels [56,57]. It requires three elements (observed, historical, and projected datasets) for analysis. However, very few studies used this technique to estimate the missing daily rainfall of the target station [58,59]. We used the observed data of the target station and that of two stations having a better correlation with the target station data and carried out EQM using R-software. QM is expressed as follows: where Qm (t) is the t th estimated daily data at the target station, Fo −1 is the inverse cumulative distribution function (CDF) of the available data at the target station, Qs (t) is the t th daily data at the neighboring station, and Fs is the CDF of the daily data at the neighboring station.

Empirical Quantile Mapping Plus (EQM + ).
In this study, we used the name "empirical quantile mapping plus (EQM + )" to refer to the empirical quantile mapping applied to the outputs (values estimated by all six techniques). e study [31] obtained a better result (reduced mean absolute error) after applying quantile mapping on the outputs generated by other techniques. us, we applied it to evaluate its performance on the outputs obtained by other techniques. First, the data matrix was made between the observed, an average of observed data, and the outputs of SAM, NRM, CCW, MLR, IDW, and EQM. en, the data matrix was refed to R-software for the empirical quantile mapping process. Finally, the output was subjected to cross-validation analysis against preset criteria.

Performance Evaluation of Gap-Filling Techniques.
Cross-validation was assessed by comparing the observed data and the data estimated by different gap-filling techniques. It was used to evaluate the quality (performance) of different gap-filling techniques based on four commonly used statistical validation (evaluation) criteria. e considered evaluation criteria are mean absolute error (MAE), root mean square error (RMSE), skill score (SS), and Pearson's correlation coefficients (R). Similar evaluation criteria were considered in identical studies conducted by [60][61][62]. e best-performing technique was selected based on cross-checking its performances under many criteria. e gap-filling techniques were evaluated as the best performing under three different conditions. e first condition (default) to decide the gap-filling techniques as best performing was when the technique has the lowest mean absolute error (MAE) and root mean square error (RMSE) and the highest skill score (SS) and correlation coefficient (R). Next, when the estimation technique fulfilled three evaluation criteria out of the four. e last condition was when the estimation technique fulfilled two evaluation criteria and showed at least equal performance level with other good performing techniques at least in one criterion. On the other hand, no gap-filling technique was decided as best performing under conditions other than these three. A similar procedure was followed to evaluate whether the application of empirical quantile mapping plus (EQM + ) improved the performances of gap-filling techniques or not.
where Vest i and Vobs i are the estimated and observed i th values, respectively, AVobs and AVest are the average of observed and estimated values, respectively, and n is the number of data points. MAE, RMSE, SS, and R are the mean absolute error, root mean squared error, skill score, and Pearson's correlation coefficient, respectively.

Performances of Gap-Filling Techniques in the Areka
Meteorological Station. e multiple linear regression (MLR) gap-filling technique outperformed other techniques under the root mean square error (RMSE), skill scores (SS), and Pearson's correlation coefficient (R) evaluation criteria in Areka station (see Table 2). It showed the lowest RMSE (7.75 mm) and the highest SS (0.16) and R (0.29). Its performance of estimating observed rainfall was appreciable up to the year 2010; however, it became poor after 2010 as indicated by its largest MAE value (see Table 2 and Figure 3(a)). Except for the empirical quantile mapping (EQM), the rest of the gap-filling methods showed comparable (similar) and second-ranked performance. It is only EQM that showed the negative (poor value) of skill scores (SS � −0.31).
e performance levels of gap-filling techniques became poor after empirical quantile mapping plus: all the techniques overestimated the observed values (see Table 2 and Figure 3(b)). Despite its poor performance after 2010, no other gap-filling techniques (including EQM + ) have comparable performance in Areka station. So, MLR gapfilling technique can be used to fill rainfall data gaps in Areka station.

Performances of Gap-Filling Techniques in Bele Station.
As in Areka station, MLR outperformed other techniques by considering three evaluation criteria in Bele station (RMSE, SS, and R) (see Table 3). e lowest RMSE (7.43 mm) and the highest SS (0.11) and R (0. 33 Table 3 and Figure 4(a)). Besides, no other techniques obtained the positive value of the skill score except MLR. Except for EQM, the rest of the gap-filling techniques showed similar performance (no significant variation in their statistics) and ranked second. Similarly, they (except for EQM) showed comparable performance with MLR in estimating the annual total rainfall of Bele station up to the year 2002 (see Figure 4(a)). us, these techniques could be used if the data required are up to the year 2002 only; otherwise, MLR is suggested to fill rainfall data gaps in Bele station. But, the performance levels of all gap-filling techniques became poorer after the application of empirical quantile mapping plus (see Figure 4(b)). All of the techniques overestimated the annual total rainfall of Bele station after EQM + . us, using EQM + is not advisable to fill the rainfall data gaps in Bele station.

Performances of Gap-Filling Techniques in Boditi-School
Station. Under the three evaluation criteria (RMSE, SS, and R), MLR showed the best performance in Boditi-School station. e lowest RMSE (7.01 mm) and the highest SS (0.2) and R (0.45) were observed in MLR (see Table 4). e yellow line of MLR showed a consistent performance in estimating the observed annual total rainfall (OBS: red line) throughout the estimation period except for (2006-2007 and 2014-2015) in Boditi-School station (see Figure 5(a)). e remaining techniques overestimated the observed annual total rainfall between 1992 and 2000 (see Figure 5(a)). e poorest performance was observed in EQM (the only technique with the negative values of SS). Except for MLR and EQM, the performance levels of all techniques were improved after applying EQM + up to the year 2005 and became poorer after 2005 (see Figure 5(b). Due to the limited improvement in the performance levels of gap-filling techniques, EQM + is not suggested for use in Boditi-School station.

Performances of Gap-Filling Techniques in Hosana
Station.
e outperformance of MLR was observed under all (MAE, RMSE, SS, and R) evaluation criteria in Hosana station (see Table 5). MLR has the lowest MAE (3.37 mm) and RMSE (5.69 mm) and the highest SS (0.37) and R (0.69). Its performance in estimating the observed daily rainfall data was consistent with time up to 2010 and decreased after 2010 (see Figure 6(a)). However, it showed poorer performance after empirical quantile mapping plus (see Figure 6(b)). Except for EQM, the rest of the gap-filling techniques showed similar performance under all of the considered evaluation criteria (see Table 5). e performance levels of four techniques (SAM2, NRM2, CCW2, and IDW2) were improved up to the year 2001 (see Figure 6(b)). e poorest performance was observed in EQM (the only technique with a negative SS value) both before and after EQM + (underestimated the observed rainfall). EQM + did not improve the values of a Person's correlation coefficient (R) in all techniques. Due to the absence of weighty improvements in performance levels of gap-filling techniques after EQM + , its application is not suggested in Hosana station.   Figure 3: Performance consistency of gap-filling techniques in estimating the observed annual total rainfall in millimeter (OBS) before (a) and after (b) quantile mapping plus (EQM + ) in Areka station. e performance of gap-filling methods after EQM + is expressed with an extension of number 2 (e.g., SAM to SAM2).

Performances of Gap-Filling Techniques in Shone Station.
MLR also outperformed other techniques in estimating the annual total rainfall of Shone station (see Table 6). However, it showed poor performance between 1992 and 1998 (see Figure 7(a)), which is expressed in its highest value of MAE (4.4 mm). Except for EQM, the rest of the gap-filling techniques showed similar performance in Shone station. e performance levels of gap-filling techniques were not improved after the application of empirical quantile mapping plus (Figure 7(b)). All of the considered techniques failed to catch the highest and lowest rainfall values of observed data between 1992 and 1998 in Shone station (see Figures 7(a) and 7(b)). When compared with other stations, all of the gap-filling techniques showed the poorest performance in Shone station.

Discussion
Evaluating the performances of gap-filling techniques at station levels has paramount benefits. MLR outperformed other techniques in all of the considered (five) meteorological stations in Wolaita Zone and the surroundings. e  Figure 4: Performance consistency of gap-filling techniques in estimating the observed annual total rainfall in millimeter (OBS) before (a) and after (b) quantile mapping plus (EQM + ) in Bele station. e performance of gap-filling methods after EQM + is expressed with an extension of number 2 (e.g., SAM to SAM2).  [67]. Teegavarapu [68] also appreciated the performance of MLR in estimating the daily rainfall of Kentucky in the USA but did not suggest using it due to its negative correlation coefficient.  With little variations between stations, four of the gapfilling techniques (SAM, NRM, CCW, and IDW) ranked second in estimating the observed rainfall in the Wolaita Zone and the surroundings. Empirical quantile mapping showed the poorest performance in all of the five stations. It is the only technique that showed the negative skill scores values in all stations. Empirical quantile mapping plus (EQM + ) improved the performance levels of some gapfilling techniques, though the improvement is not substantial. However, it did not improve the performance level of MLR in any of the five stations. ere was a statistically nonsignificant difference in the relative performance of gap-filling techniques between stations. is is because all stations have a similar rainfall pattern of the bimodal (peak and valley). Besides, their statistics of variation between the observed and mean values (standard deviation) between stations are comparable (53.94-68.7 mm) (see Table 1).
To determine the relationships between the altitude of meteorological stations and performance levels of the techniques, Pearson's correlation was analyzed. e results indicated that there was a strong negative correlation between altitude and MAE (−0.91) and between altitude and RMSE (−0.72). Besides, a strong positive correlation was obtained between altitude and SS (0.82) and between altitude  Figure 6: Performance consistency of gap-filling techniques in estimating the observed annual total rainfall in millimeter (OBS) before (a) and after (b) quantile mapping plus (EQM + ) in Hosana station. e performance of gap-filling methods after EQM + is expressed with an extension of number 2 (e.g., SAM to SAM2).

Advances in Meteorology 11
and R (0.75). is showed that the gap-filling techniques have better performance in meteorological stations located at a higher altitude than those at lower altitudes. is is because the meteorological stations located in higher elevations obtain more rainfall in a better pattern (better data statistics) and those located in lower altitudes received erratic rainfall. e preference to use any of the tested gapfilling techniques has to consider the performances of each technique in each station. In general, MLR without EQM + can be suggested for use in the study area. It is in agreement with the study [69] indicating that the precision of MLR in estimating the observed rainfall is less affected by the increase of failure (percent of missing data) and has better performance when the distance between stations is short.

Conclusion
e performances of seven gap-filling techniques in estimating the daily observed rainfall data in five meteorological stations of Wolaita Zone and the surrounding were tested in this study. e techniques were tested against the four widely used evaluation criteria such as mean absolute error (MAE), root mean square error (RMSE), skill score (SS), and Pearson's correlation coefficients (R). MLR fulfilled three of Figure 7: Performance consistency of gap-filling techniques in estimating the observed annual total rainfall in millimeter (OBS) before (a) and after (b) quantile mapping plus (EQM + ) in the Shone station. e performance of gap-filling methods after EQM + is expressed with an extension of number 2 (e.g., SAM to SAM2). the evaluation criteria (RMSE, SS, and R) in all of the five meteorological stations in Wolaita Zone and the surroundings. It showed the lowest RMSE and the highest SS and R over all of the considered techniques. With some exceptional cases, its performance was consistent with the analysis period . None of the remaining methods has comparable performance with MLR. However, its performance becomes poorer after the empirical quantile mapping plus applied. Except for EQM, the rest of the gapfilling techniques (SAM, NRM, CCW, and IDW) did not show a statistically significant difference in their performance levels in all of the considered stations. us, prioritizing any of these four techniques depends on the intended analysis period, the purpose of end-use, and individual station. EQM showed the poorest performance under all of the evaluation criteria in all of the stations. Besides, its application on the outputs obtained by other techniques (EQM + ) did not bring noteworthy improvements in the performance levels of gap-filling techniques. So, it is suggested to use the MLR technique to fill in the missing values of daily rainfall in the stations of Wolaita Zone and the surroundings. In addition, using any of the second-ranked techniques depending on their performance range (period and station) is acceptable to be used in the study area.
Data Availability e data of meteorological stations are available in the National Meteorological Agency (NMA) of Ethiopia, which is free for the study purpose and charged for other purposes. An official letter is needed to access the data of meteorological stations. Important datasets used for this study are included within the paper. Disclosure is paper is part of a Ph.D. dissertation work of a corresponding author supervised by co-authors.

Conflicts of Interest
e authors declare that there are no conflicts of interest concerning the publication of this article.