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

Evaluation of Seven Gap-Filling Techniques for Daily Station-Based Rainfall Datasets in South... Hindawi Advances in Meteorology Volume 2021, Article ID 9657460, 15 pages https://doi.org/10.1155/2021/9657460 Research Article Evaluation of Seven Gap-Filling Techniques for Daily Station-Based Rainfall Datasets in South Ethiopia 1,2 1 1 3 4 Alefu Chinasho , Bobe Bedadi, Tesfaye Lemma, Tamado Tana, Tilahun Hordofa, and Bisrat Elias 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 Correspondence should be addressed to Alefu Chinasho; chinalefu11@gmail.com Received 5 June 2021; Revised 21 July 2021; Accepted 13 August 2021; Published 19 August 2021 Academic Editor: Stefano Federico Copyright © 2021 Alefu Chinasho et al. &is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Meteorological stations, mainly located in developing countries, have gigantic missing values in the climate dataset (rainfall and temperature). Ignoring the missing values from analyses has been used as a technique to manage it. However, it leads to partial and biased results in data analyses. Instead, filling the data gaps using the reference datasets is a better and widely used approach. &us, this study was initiated to evaluate the seven gap-filling techniques in daily rainfall datasets in five meteorological stations of Wolaita Zone and the surroundings in South Ethiopia. &e considered gap-filling techniques in this study were simple arithmetic means (SAM), normal ratio method (NRM), correlation coefficient weighing (CCW), inverse distance weighting (IDW), multiple linear regression (MLR), empirical quantile mapping (EQM), and empirical quantile mapping plus (EQM ). &e techniques were preferred because of their computational simplicity and appreciable accuracies. &eir performance was evaluated against mean absolute error (MAE), root mean square error (RMSE), skill scores (SS), and Pearson’s correlation coefficients (R). &e results indicated that MLR outperformed other techniques in all of the five meteorological stations. It showed the lowest RMSE and the highest SS and R in all stations. Four techniques (SAM, NRM, CCW, and IDW) showed similar performance and were second-ranked in all of the stations with little exceptions in time series. EQM improved (not substantial) the performance levels of gap-filling techniques in some stations. In general, MLR is suggested to fill in the missing values of the daily rainfall time series. However, the second-ranked techniques could also be used depending on the required time series (period) of each station. &e techniques have better performance in stations located in higher altitudes. &e authors expect a substantial contribution of this paper to the achievement of sustainable development goal thirteen (climate action) through the provision of gap-filling techniques with better accuracy. predominantly caused by the provisional absence of ob- 1. Introduction servers, equipment miscarriage, data archiving, and irregular Rainfall (precipitation) is one of the key inputs in many calibration of devices [4, 5]. Ignoring the missing values disciplines such as climatology (climate variability and from analyses has been used as a technique to manage it change), meteorology (weather conditions), irrigation en- [6–8]. However, it leads to partial (coarse resolution) and gineering (irrigation scheduling), hydrology (water cycle), biased results in data analyses [9–11]. Instead, filling the data and environmental hazard assessment (floods). Despite its gaps using reference datasets such as reanalysis products or overriding uses, the rainfall dataset of meteorological sta- estimates from the surrounding stations are better and tions has gigantic missing values, mainly in developing widely used approaches [12–15]. Ample gap-filling tech- countries [1–3]. Data gaps in rainfall time series are niques have been evaluated and suggested in the literature to 2 Advances in Meteorology globe (Serially Complete Earth) dataset using the global fill in the missing daily rainfall time series at different parts of the world. &e majority of gap-filling techniques are spatial historical climatology network daily (GHCND), a global surface summary of the day (GSOD), and Environment and interpolation methods. Among the spatial interpolation techniques, simple Climate Change Canada (ECCC). In addition, Noh and Ahn arithmetic mean (SAM) was indicated for its best perfor- [39] developed a new gridded rainfall dataset (K-Hydra) mance and computational simplicity in some studies over the Korean peninsula to fill rainfall data gaps, which has [16–18]. But, [19, 20] prioritized inverse distance weighting comparable performance with global precipitation clima- (IDW) over other spatial interpolation techniques. Out- tology project (GPCP), climate prediction center (CPC), performance was also reported for the normal ratio method tropical rainfall measuring mission (TRMM), and Asian precipitation highly resolved observational data integration (NRM) [16, 21, 22], correlation coefficient weighing (CCW) [23], and multiple linear regression (MLR) [24]. Never- towards evaluation (APHRODITE). In Ethiopia, some studies evaluated and suggested dif- theless, Longman et al. [25] specified no statistical differ- ences (similar performance) between five spatial ferent gap-filling techniques for daily rainfall time series. For instance, Boke [40] evaluated five spatial gap-filling tech- interpolation techniques (normal ratio method, linear re- gression, inverse distance weighting, quantile mapping, niques in ten meteorological stations in Ethiopia and sug- and single best estimator) for large gaps. Machine learning gested the nearest neighbor, inverse distance weighting processes such as the artificial neural network (ANN), average, and modified inverse distance weighting average for Kernel approaches, and kriging are also suggested in some the country. Woldesenbet et al. [41] also tested four gap- studies to fill the rainfall data gaps. &e best performance of filling techniques in 38 stations in the upper Blue Nile basin the machine learning process was stated for ANN [26, 27], of Ethiopia in which CCW showed the best performance over NRM, modified NRM, and IDW. Similarly, Armanuos ordinary kriging [28, 29], and Kernel approaches [30]. Besides, Grillakis et al. [31] indicated the acceptable per- et al. [17] assessed twenty-one (21) gap-filling methods in 15 stations and suggested that NRM, MLR, IDW, CCW, and formance of empirical quantile mapping in filling the discontinued daily rainfall data in the Mediterranean island SAM fill in the missing rainfall data in Ethiopia. &e reviewed literature indicates that the performances of gap- of Crete. Combining or modifying the previously existing gap- filling techniques vary between stations, considered evalu- filling techniques is also reported for better performance ation criteria, statistical properties of data [17], and density than using the techniques separately. Teegavarapu et al. [32] and the geometrical organization of the station network [42]. indicated that the linear weight optimization method Yet, to the authors’ best knowledge, none of the reviewed (LWOM) with a single best estimator (SBE) performed literature and no related study covered the meteorological better than SBE only in Florida. Similarly, Kim and stations located in Wolaita Zone and the surroundings. Moreover, the applicability of gap-filling methods is limited Pachepsky [33] concluded that the regression tree (RT) with ANN showed better performance than solely using RT or by many factors including the required computational skill and the percentage of gaps in the data [43]. On the other ANN in the Chesapeake Bay watershed of the USA. Fur- thermore, Khosravi et al. [34] presented better performance hand, Ethiopia is a large country covering about 1,104,300 of the modified geographical coordinate (GC) method than square kilometers [44] in which directly using any of the the previously available methods in 24 station gauges in Iran. suggested techniques for the entire country is not repre- Mart´ınez et al. [35] also showed that the generalization of the sentative and can lead to biased results. So, testing the gap- modified normal ratio with the inverse distance weighting filling techniques at local levels is very important. and the generalization of modified correlation coefficient &us, this study was initiated to evaluate the perfor- with the inverse distance weighting method outperformed mances of seven gap-filling techniques to fill in the missing NRM, NRM weighted with correlation, NRM modified with values of daily rainfall data in the meteorological stations of Wolaita Zone and the surroundings in South Ethiopia. &e IDW, CCW, modified CCW, IDW, modified correlation coefficient with IDW, IDW weighing of NRM with corre- seven selected techniques were simple arithmetic mean (SAM), normal ratio method (NRM), inverse distance lation, and IDW-modified height. Similarly, Rahman et al. [36] indicated that the generalized linear model with gamma weighting (IDW), correlation coefficient weighing (CCW), and Fourier series was outperformed over SAM, NRM, multiple linear regression (MLR), empirical quantile map- CCW, and IDW in estimating the missing daily rainfall ping (EQM), and empirical quantile mapping plus (EQM ). series. &e Gaussian mixture model-based KNN imputation &e techniques were preferred among others due to their showed better performance level than KNN only [37]. computational simplicity, wider application, and compa- Filling the rainfall data gaps using the reanalysis prod- rable performance with other techniques [45]. Performances ucts is also another widely used approach. For example, of the techniques were tested against four evaluation criteria Cordeiro and Blanco [38] indicated that the Climate Haz- such as mean absolute error (MAE), root mean square error ards Group InfraRed Precipitation with Stations (CHIRPS) (RMSE), skill score (SS), and Pearson’s correlation coeffi- product outperformed the tropical rainfall measuring mis- cients. As well, the performance consistency was evaluated sion (TRMM) and Morphing Technique (CMORPH-CPC) on different time scales. in estimating daily rainfall time series in the Amazon region. &e authors of this paper expect momentous contri- Further, Tang et al. [14, 15] filled the data gaps in daily butions of the paper to environmentalists, engineers, cli- rainfall of North America (serially complete NA) and the matologists, agriculturalists, and natural resource Advances in Meteorology 3 management experts facing rainfall data gaps. &e tech- from February and March to December. It ranges between ° ° niques included in this study can be tracked on any other 8.65 C (in Hosana) and 15.4 C (in Areka) (see Table 1). location and their performances can be compared with the findings of this work. Besides, the filled rainfall datasets of 2.2. Methodology. &e methodology of this work trailed the five meteorological stations (Areka, Bele, Boditi, Hosana, following processing steps. First, the data matrixes of five and Shone) are freely available based on requests. Moreover, stations with complete data (excluding the years of data our findings have a substantial contribution to sustainable missing) were prepared. For the gap-filling techniques other development goal (SDG) thirteen (climate action) by pro- than quantile mapping and quantile mapping plus, the viding the filled and summarized rainfall data freely so that datasets of five (all) stations were considered. In the em- the policymakers of the country can use it to understand the pirical quantile mapping (EQM and EQM ), the datasets of climate variability and change in the study area with reduced three stations (one target and two with higher correlation error level. So, it provides imperative information to take coefficients) were used. &e correlation between a target action on climate change adaptation and mitigation mea- station and the surrounding stations is more important than sures. &e rest part of this paper is organized into four proximity (physical distance) of the stations [25]. &en, the sections. Section 2 describes the materials and methods: seven gap-filling techniques were cross-validated using four study area and data description and methodology for gap- evaluation criteria, and the missing values were estimated filling techniques and evaluation criteria. Section 3 presents using the best-performed technique. In the case when there the results of the gap-filling techniques of the missing daily is no data from neighboring stations, the method used by precipitation data in five meteorological stations. Section 4 Ismail and Ibrahim [50], using the mean on the same day discusses and interprets the results. Finally, Section 5 con- and month but at different years, was used to estimate the cludes the findings of this study. missing value on that particular date. &e detailed meth- odology is described in the following paragraphs. 2. Materials and Methods 2.1. Study Area and Data Description. Five meteorological 2.2.1. Simple Arithmetic Mean (SAM). It estimates the stations located in two zones (Wolaita and Hadiya) of missing values in the target station from the surrounding southern nations’ nationalities and people’s regional state of stations by simply taking the average of surrounding stations’ Ethiopia were included in this study (see Figure 1). From the data in the same period of missing value [51]. &is is the five stations, two (Hosana and Shone) are located in Hadiya simplest technique of estimating missing values used when Zone and three stations (Areka, Bele, and Boditi) are located the missing value has less than 10% [52]. It is expressed as in Wolaita Zone. &e five meteorological stations considered 􏽐 V in this study are sufficient and comparable with the four i�1 i (1) V � , stations [46, 47] and six stations [48] of similar studies. &e n stations are located from 6.92 to 7.57 (latitude) and from 37.5 where V is the estimated value of the missing data, V is the o i to 37.95 (longitude) and in the altitudinal ranges of th value of the same variable at the i nearest station, and n is the 1240–2397 meters above sea level (see Table 1). &e observed number of nearest weather stations considered for averaging. daily rainfall and maximum and minimum temperature data of five stations for periods (1987–2017) were obtained from the National Meteorological Agency (NMA) of Ethiopia [49]. 2.2.2. Normal Ratio Method (NRM). It considers the cor- &e stations have huge missing values up to 30.2% in relation coefficients between the target station and the sur- daily rainfall, 29.4% in maximum temperature, and 19.4% in rounding stations. It is recommended for filling in missing minimum temperature (see Table 1). Besides, Bele and values if more than 10% of the data is missing [52]. It gives Shone stations did not have the dataset for maximum and weight to the data of surrounding stations based on their minimum temperature in the study period. So, the two correlation with the target station. It is expressed as follows: stations were not considered in analyses of maximum and 􏽐 W V i�1 i i minimum temperature (see Table 1). &e rainfall datasets of V � , (2) o n 􏽐 W five stations have a bimodal pattern (two peaks in the year) i�1 even though the months of obtaining peak values slightly where V is the estimated value, W depicts the weight of the o i vary from station to station (see Figure 2, presented in bar th i surrounding weather station, and V is the value of the charts). Two peak values of rainfall were observed in April th same variable at the i station. &e weight of the sur- and August in Areka and Hosana stations, April and July in rounding station is calculated using the following equation: Shone, May and August in Boditi, and May and July in Bele stations. &e study area received an annual rainfall between n − 2 W � r 􏼠 􏼡, (3) i 2 1,212 (in Hosana) and 1,561 mm (in Shone). Besides, the 1 − r maximum temperature has a bimodal distribution pattern th (see Figure 2: presented in lines). &e mean monthly where W is the weight of the i station, r corresponds to the th maximum temperature varies between 19.34 C (in Hosana) correlation coefficient between the target station and the i and 29.5 C (in Areka) (see Table 1). &e minimum tem- surrounding station, and n is the number of points used to perature of the area has a continuously decreasing trend calculate the correlation coefficient. 4 Advances in Meteorology 240000 280000 320000 360000 400000 440000 850000 850000 820000 820000 790000 790000 760000 760000 730000 730000 Scale: 1:1,200,000 240000 280000 320000 360000 400000 440000 Stations National Selected Zones Selected Zones in SNNPRS Figure 1: Location map of five meteorological stations in Wolaita Zone and the surroundings. SNNPRS is southern nations’ nationalities’ and peoples’ regional state of Ethiopia. Table 1: Description of five meteorological stations in Wolaita Zone and the surroundings. Stations Geographic information Areka Bele Boditi Hosana Shone Latitude (degree) 7.07 6.92 6.95 7.57 7.13 Longitude (degree) 37.7 37.53 37.96 37.85 37.95 Altitude (meter) 1804 1240 2043 2307 1959 Rainfall Data coverage 1988/2017 1987–2018 1987–2018 1987–2018 1987–2018 Missing data (%) 30.2 21.5 4.5 2.7 8.4 Monthly total value 1536.84 1250.16 1264.66 1212.34 1560.58 Minimum value 29.54 28.74 34.72 11.92 37.06 Maximum value 209.1 174.44 182.08 165.66 235.94 Mean value 128.07 104.18 105.4 101.03 130.05 Standard deviation 68.7 61.13 53.94 55.1 68.63 Maximum temperature Data coverage 1992–2017 NA 1987–2018 1987–2018 NA Missing data (%) 29.4 NA 4.6 14.8 NA Minimum value 22.2 NA 21 19.34 NA Maximum value 29.5 NA 28.4 25.6 NA Advances in Meteorology 5 Table 1: Continued. Stations Geographic information Areka Bele Boditi Hosana Shone Mean value 25.7 NA 25 22.7 NA Standard deviation 2.5 NA 2.5 2.14 NA Minimum temperature Data coverage 1992–2017 NA 1987–2018 1987–2018 NA Missing data (%) 19.36 NA 4.7 12.5 NA Minimum value 12.95 NA 11.99 8.65 NA Maximum value 15.44 NA 14.29 12.03 NA Mean value 14.14 NA 13.28 10.81 NA Standard deviation 0.72 NA 0.75 0.95 NA NA is data not available. 250.0 200.0 150.0 100.0 50.0 0.0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec RF_Areka RF_Shone Tmin_Areka RF_Hosana Tmax_Areka Tmin_Boditi RF_Bele Tmax_Boditi Tmin_Hosana RF_Boditi Tmax_Hosana Figure 2: Mean monthly annual rainfall and temperature (maximum and minimum) patterns in Wolaita Zone and the surroundings. RF is ° ° the total rainfall (mm), Tmax is the mean maximum temperature ( C), and Tmin is the mean minimum temperature ( C). 2.2.3. Inverse Distance Weighting (IDW). It is the most where V is the estimate obtained for missing value, V is the o i th th commonly used technique for estimating the missing values observed value at the i station, d is the i surrounding of daily rainfall [53]. It assumes that the closer the sur- station distance, and n is the number of stations used. &e rounding stations to the target station, the better the esti- distance between the target station and the surrounding mation of missing values and the lower the error in stations is calculated using the Pythagoras formula. estimation or the better the accuracy. It is calculated using 􏽱������������������� 2 2 (5) the following equation d � X − X􏼁 + Y − Y􏼁 , i a i a i 􏽐 V /d i�1 i i where d is the distance between the target station and the V � , (4) i o n th 􏽐 1/d􏼁 i�1 surrounding i station, X and X are the longitudes, and Y a i a Rainfall (mm) and Temperature (°C) 6 Advances in Meteorology th th and Y are the latitudes of the target and the i surrounding where Qm (t) is the t estimated daily data at the target −1 stations, respectively. &en, the values in degrees are mul- station, Fo is the inverse cumulative distribution function tiplied by 111 to convert them to kilometers. (CDF) of the available data at the target station, Qs (t) is the th t daily data at the neighboring station, and Fs is the CDF of the daily data at the neighboring station. 2.2.4. Correlation Coefficient Weighing (CCW). In this ap- proach, distance is replaced by Pearson’s correlation coef- ficients [54]. It assures that the datasets of surrounding 2.2.7. Empirical Quantile Mapping Plus (EQM ). In this stations having a better positive correlation with that of the study, we used the name “empirical quantile mapping plus target station give better estimates of missing values in target (EQM )” to refer to the empirical quantile mapping ap- stations than that of less correlated ones. &us, Pearson’s plied to the outputs (values estimated by all six tech- correlation coefficients between rainfall data of five mete- niques). &e study [31] obtained a better result (reduced orological stations were analyzed, and the missing values in mean absolute error) after applying quantile mapping on target stations were determined using the following the outputs generated by other techniques. &us, we ap- equation: plied it to evaluate its performance on the outputs obtained by other techniques. First, the data matrix was made be- 􏽐 r V i�1 i i tween the observed, an average of observed data, and the V � , (6) o n 􏽐 r i�1 outputs of SAM, NRM, CCW, MLR, IDW, and EQM. &en, the data matrix was refed to R-software for the where V is the missing value of the target station, r is the th empirical quantile mapping process. Finally, the output correlation coefficient of the i surrounding station, and V is th was subjected to cross-validation analysis against preset the value of the same variable in the i surrounding station. criteria. 2.2.5. Multiple Linear Regression (MLR). It was carried out by considering the linear significant relationship between 2.3. Performance Evaluation of Gap-Filling Techniques. the observed values of the target station and the surrounding Cross-validation was assessed by comparing the observed data and the data estimated by different gap-filling tech- stations [55]. &e dataset of the target station was considered as a dependent variable and the surrounding stations’ niques. It was used to evaluate the quality (performance) of different gap-filling techniques based on four commonly datasets were considered as independent variables. Ac- cordingly, the multiple linear regressions were carried out used statistical validation (evaluation) criteria. &e con- sidered evaluation criteria are mean absolute error (MAE), for five stations. &en, the missing values in the target station were filled using the intercept and the coefficients of the root mean square error (RMSE), skill score (SS), and variables were expressed as follows: Pearson’s correlation coefficients (R). Similar evaluation criteria were considered in identical studies conducted by [60–62]. &e best-performing technique was selected based V � a + 􏽘 a V􏼁 , (7) o 0 i i i�1 on cross-checking its performances under many criteria. &e gap-filling techniques were evaluated as the best where V is the estimated value, a , a , . . . , a are regression o 0 i n performing under three different conditions. &e first coefficients, and V is the value of the same parameter at the condition (default) to decide the gap-filling techniques as th i weather station. 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 2.2.6. Empirical Quantile Mapping (EQM). It is a very coefficient (R). Next, when the estimation technique ful- common technique used to downscale the global circulation filled three evaluation criteria out of the four. &e last model (GCM) outputs of rainfall to the regional and local condition was when the estimation technique fulfilled two levels [56, 57]. It requires three elements (observed, his- evaluation criteria and showed at least equal performance torical, and projected datasets) for analysis. However, very level with other good performing techniques at least in one few studies used this technique to estimate the missing daily criterion. On the other hand, no gap-filling technique was rainfall of the target station [58, 59]. We used the observed decided as best performing under conditions other than data of the target station and that of two stations having a these three. A similar procedure was followed to evaluate better correlation with the target station data and carried out whether the application of empirical quantile mapping plus EQM using R-software. QM is expressed as follows: (EQM ) improved the performances of gap-filling tech- −1 Qm(t) � Fo [Fs[Qs(t)]], (8) niques or not. Advances in Meteorology 7 Vobs − Vest 􏽐 􏼁 i�1 i i MAE � , 􏽳����������������� � n 2 􏽐 Vobs − Vest 􏼁 i�1 i i RMSE � , MSE(Vest, Vobs) SS(Vest, Vobs and AVobs) � 1 − , MSE(Vavg, Vobs) (9) n 2 􏽐 Vest − Vobs 􏼁 i i i�1 MSE(Vest, Vobs) � , 􏽐 Vavg − Vobs 􏼁 i�1 i MSE(AVobs, Vobs) � , 􏽐 Vobs − AVobs􏼁∗ Vest − AVest􏼁 1 i i 􏽱��������������������������������������� R � , 2 2 n n 􏽐 Vobs − AVobs ∗ 􏽐 Vest − AVest 􏼁 􏼁 i�1 i i�1 i th where Vest and Vobs are the estimated and observed i (yellow line) was outperformed in estimating the observed i i values, respectively, AVobs and AVest are the average of annual total rainfall (red line) of Bele station in all the years observed and estimated values, respectively, and n is the (1988–2017) (see Table 3 and Figure 4(a)). Besides, no other number of data points. MAE, RMSE, SS, and R are the mean techniques obtained the positive value of the skill score absolute error, root mean squared error, skill score, and except MLR. Except for EQM, the rest of the gap-filling Pearson’s correlation coefficient, respectively. techniques showed similar performance (no significant variation in their statistics) and ranked second. Similarly, they (except for EQM) showed comparable performance 3. Results with MLR in estimating the annual total rainfall of Bele 3.1. Performances of Gap-Filling Techniques in the Areka station up to the year 2002 (see Figure 4(a)). &us, these techniques could be used if the data required are up to the Meteorological Station. &e multiple linear regression year 2002 only; otherwise, MLR is suggested to fill rainfall (MLR) gap-filling technique outperformed other techniques data gaps in Bele station. But, the performance levels of all under the root mean square error (RMSE), skill scores (SS), gap-filling techniques became poorer after the application of and Pearson’s correlation coefficient (R) evaluation criteria empirical quantile mapping plus (see Figure 4(b)). All of the in Areka station (see Table 2). It showed the lowest RMSE techniques overestimated the annual total rainfall of Bele (7.75 mm) and the highest SS (0.16) and R (0.29). Its per- + + station after EQM . &us, using EQM is not advisable to fill formance of estimating observed rainfall was appreciable up the rainfall data gaps in Bele station. 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 3.3. Performances of Gap-Filling Techniques in Boditi-School (EQM), the rest of the gap-filling methods showed com- Station. Under the three evaluation criteria (RMSE, SS, and parable (similar) and second-ranked performance. It is only R), MLR showed the best performance in Boditi-School EQM that showed the negative (poor value) of skill scores station. &e lowest RMSE (7.01 mm) and the highest SS (SS � −0.31). &e performance levels of gap-filling tech- (0.2) and R (0.45) were observed in MLR (see Table 4). &e niques became poor after empirical quantile mapping plus: yellow line of MLR showed a consistent performance in all the techniques overestimated the observed values (see estimating the observed annual total rainfall (OBS: red line) Table 2 and Figure 3(b)). Despite its poor performance after throughout the estimation period except for (2006-2007 2010, no other gap-filling techniques (including EQM ) have and 2014-2015) in Boditi-School station (see Figure 5(a)). comparable performance in Areka station. So, MLR gap- &e remaining techniques overestimated the observed filling technique can be used to fill rainfall data gaps in Areka annual total rainfall between 1992 and 2000 (see station. Figure 5(a)). &e poorest performance was observed in EQM (the only technique with the negative values of SS). 3.2. Performances of Gap-Filling Techniques in Bele Station. Except for MLR and EQM, the performance levels of all As in Areka station, MLR outperformed other techniques by techniques were improved after applying EQM up to the considering three evaluation criteria in Bele station (RMSE, year 2005 and became poorer after 2005 (see Figure 5(b). SS, and R) (see Table 3). &e lowest RMSE (7.43 mm) and the Due to the limited improvement in the performance levels highest SS (0.11) and R (0.33) values were observed in MLR. of gap-filling techniques, EQM is not suggested for use in Except for the periods 1988–1991 and 2004–2009, MLR Boditi-School station. 8 Advances in Meteorology Table 2: Performance evaluation results of gap-filling techniques in Areka station before and after empirical quantile mapping plus (EQM ). Gap-filling techniques Performance evaluation criteria SAM NRM CCW IDW MLR EQM Before empirical quantile mapping plus MAE (mm) 4.16 4.14 4.15 4.21 4.67 5.40 RMSE (mm) 7.96 7.98 7.96 8.04 7.75 9.70 SS (unitless) 0.12 0.11 0.12 0.10 0.16 −0.31 R (unitless) 0.29 0.29 0.29 0.29 0.29 0.22 After empirical quantile mapping plus (EQM ) MAE (mm) 5.01 4.98 5.00 5.06 5.74 6.29 RMSE (mm) 8.11 8.12 8.10 8.21 7.99 10.08 SS (unitless) 0.08 0.08 0.09 0.06 0.11 −0.42 R (unitless) 0.29 0.29 0.29 0.30 0.27 0.22 MAE, RMSE, SS, and R are mean absolute error, root mean square error, skill score, and Person’s correlation coefficients, respectively. 2000 2400 1200 1400 400 400 OBS CCW MLR OBS CCW2 MLR2 SAM IDW EQM SAM2 IDW2 EQM2 NRM NRM2 (a) (b) 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). 3.4. Performances of Gap-Filling Techniques in Hosana considered evaluation criteria (see Table 5). &e perfor- Station. &e outperformance of MLR was observed under mance levels of four techniques (SAM2, NRM2, CCW2, and IDW2) were improved up to the year 2001 (see all (MAE, RMSE, SS, and R) evaluation criteria in Hosana station (see Table 5). MLR has the lowest MAE (3.37 mm) Figure 6(b)). &e poorest performance was observed in and RMSE (5.69 mm) and the highest SS (0.37) and R EQM (the only technique with a negative SS value) both (0.69). Its performance in estimating the observed daily before and after EQM (underestimated the observed rainfall data was consistent with time up to 2010 and rainfall). EQM did not improve the values of a Person’s decreased after 2010 (see Figure 6(a)). However, it showed correlation coefficient (R) in all techniques. Due to the poorer performance after empirical quantile mapping plus absence of weighty improvements in performance levels of (see Figure 6(b)). Except for EQM, the rest of the gap-filling gap-filling techniques after EQM , its application is not techniques showed similar performance under all of the suggested in Hosana station. Annual Rainfall (mm) Annual Rainfall (mm) 2016 Advances in Meteorology 9 Table 3: Performance evaluation results of gap-filling techniques in Bele station before and after empirical quantile mapping plus. Gap-filling techniques Performance evaluation criteria SAM NRM CCW IDW MLR EQM Before empirical quantile mapping plus MAE (mm) 4.38 4.37 4.37 4.47 4.47 5.21 RMSE (mm) 7.91 7.95 7.92 8.13 7.43 10.18 SS (unitless) −0.01 −0.02 −0.02 −0.07 0.11 −0.68 R (unitless) 0.33 0.33 0.33 0.32 0.33 0.23 After empirical quantile mapping plus (EQM ) MAE (mm) 4.51 4.48 4.49 4.59 4.75 5.33 RMSE (mm) 8.03 8.06 8.03 8.25 7.44 10.25 SS (unitless) −0.04 −0.05 −0.04 −0.10 0.11 −0.70 R (unitless) 0.33 0.33 0.33 0.32 0.33 0.24 MAE, RMSE, SS, and R, are mean absolute error, root mean square error, skill score, and Person’s correlation coefficients, respectively. OBS CCW2 MLR2 OBS CCW MLR SAM2 IDW2 EQM2 SAM IDW EQM NRM2 NRM (a) (b) 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). 3.5. Performances of Gap-Filling Techniques in Shone Station. observed data between 1992 and 1998 in Shone station (see MLR also outperformed other techniques in estimating the Figures 7(a) and 7(b)). When compared with other stations, all of the gap-filling techniques showed the poorest per- annual total rainfall of Shone station (see Table 6). However, it showed poor performance between 1992 and 1998 (see formance in Shone station. Figure 7(a)), which is expressed in its highest value of MAE (4.4 mm). Except for EQM, the rest of the gap-filling 4. Discussion techniques showed similar performance in Shone station. &e performance levels of gap-filling techniques were not Evaluating the performances of gap-filling techniques at improved after the application of empirical quantile map- station levels has paramount benefits. MLR outperformed ping plus (Figure 7(b)). All of the considered techniques other techniques in all of the considered (five) meteorological failed to catch the highest and lowest rainfall values of stations in Wolaita Zone and the surroundings. &e Annual Rainfall (mm) Annual Rainfall (mm) 2016 10 Advances in Meteorology Table 4: &e performance evaluation result of gap-filling techniques in Boditi-School station before and after empirical quantile mapping plus. Gap-filling techniques Performance evaluation criteria SAM NRM CCW IDW MLR EQM Before empirical quantile mapping plus MAE (mm) 3.82 3.84 3.83 3.89 3.83 4.11 RMSE (mm) 7.22 7.23 7.21 7.33 7.01 8.65 SS (unitless) 0.15 0.15 0.15 0.13 0.20 −0.22 R (unitless) 0.44 0.45 0.45 0.43 0.45 0.31 After empirical quantile mapping plus (EQM ) MAE (mm) 3.39 3.39 3.38 3.44 3.24 3.84 RMSE (mm) 7.14 7.13 7.13 7.23 7.17 8.48 SS (unitless) 0.17 0.17 0.17 0.15 0.16 −0.17 R (unitless) 0.44 0.44 0.44 0.43 0.45 0.30 MAE, RMSE, SS, and R are mean absolute error, root mean square error, skill score, and Person’s correlation coefficients, respectively. OBS CCW MLR OBS CCW2 MLR2 SAM IDW EQM SAM2 IDW2 EQM2 NRM NRM2 (a) (b) Figure 5: 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 Boditi-School station. &e performance of gap-filling methods after EQM is expressed with an extension of number 2 (e.g., SAM to SAM2). outperformance of MLR in estimating the observed rainfall rainfall [65, 66], yet MLR considers the linear relationships data was also observed in meteorological stations of southern between the observed and estimated values. Besides, MLR Iran [63] and South Central Chile [64]. In the study area, MLR increased the number of rainy days (i.e., no zero was obtained estimates the daily observed rainfall with the mean absolute in estimates of MLR) which limited its performance. &e poor error of 4.67 mm in Areka, 4.47 mm in Bele, 3.83 mm in performance of MLR in estimating the observed daily rainfall Boditi-School, 3.37 mm in Hosana, and 4.4 mm in Shone dataset was observed in China under MAE and RMSE stations. In some years in the considered period (1988–2017), evaluation criteria [67]. Teegavarapu [68] also appreciated the MLR showed poorer performances like failure to catch ex- performance of MLR in estimating the daily rainfall of treme values. &e inconsistency of the MLR performance is Kentucky in the USA but did not suggest using it due to its associated with the conditional (inconsistent) process of negative correlation coefficient. Annual Rainfall (mm) Annual Rainfall (mm) 2016 Advances in Meteorology 11 Table 5: Performance evaluation results of gap-filling techniques in Hosana station before and after empirical quantile mapping plus. Gap-filling techniques Performance evaluation criteria SAM NRM CCW IDW MLR EQM Before empirical quantile mapping plus MAE (mm) 3.85 3.84 3.84 3.86 3.37 3.89 RMSE (mm) 7.14 7.14 7.14 7.16 5.69 8.37 SS (unitless) 0.01 0.01 0.01 0.00 0.37 −0.36 R (unitless) 0.38 0.38 0.38 0.38 0.69 0.28 After empirical quantile mapping plus (EQM ) MAE (mm) 3.48 3.47 3.47 3.49 3.16 3.64 RMSE (mm) 6.86 6.86 6.86 6.87 6.00 8.00 SS (unitless) 0.08 0.08 0.08 0.08 0.30 −0.25 R (unitless) 0.37 0.37 0.37 0.37 0.69 0.26 MAE, RMSE, SS, and R are mean absolute error, root mean square error, skill score, and Person’s correlation coefficients, respectively. 1800 1700 1600 1500 1200 1100 1000 900 800 700 600 500 OBS CCW MLR OBS CCW2 MLR2 SAM IDW EQM SAM2 IDW2 EQM2 NRM NRM2 (a) (b) 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). With little variations between stations, four of the gap- filling techniques between stations. &is is because all sta- filling techniques (SAM, NRM, CCW, and IDW) ranked tions have a similar rainfall pattern of the bimodal (peak and second in estimating the observed rainfall in the Wolaita valley). Besides, their statistics of variation between the Zone and the surroundings. Empirical quantile mapping observed and mean values (standard deviation) between showed the poorest performance in all of the five stations. It stations are comparable (53.94–68.7 mm) (see Table 1). is the only technique that showed the negative skill scores To determine the relationships between the altitude of values in all stations. Empirical quantile mapping plus meteorological stations and performance levels of the (EQM ) improved the performance levels of some gap- techniques, Pearson’s correlation was analyzed. &e results filling techniques, though the improvement is not sub- indicated that there was a strong negative correlation be- stantial. However, it did not improve the performance level tween altitude and MAE (−0.91) and between altitude and of MLR in any of the five stations. &ere was a statistically RMSE (−0.72). Besides, a strong positive correlation was nonsignificant difference in the relative performance of gap- obtained between altitude and SS (0.82) and between altitude Annual Rainfall (mm) Annual Rainfall (mm) 2016 12 Advances in Meteorology Table 6: Performance evaluation results of gap-filling techniques in Shone station before and after empirical quantile mapping plus. Gap-filling techniques Performance evaluation criteria SAM NRM CCW IDW MLR EQM Before empirical quantile mapping plus MAE (mm) 4.0 4.0 4.0 4.0 4.4 4.3 RMSE (mm) 7.3 7.3 7.3 7.4 6.9 8.5 SS (unitless) 0.1 0.1 0.1 0.0 0.2 −0.3 R (unitless) 0.4 0.4 0.4 0.4 0.4 0.3 After empirical quantile mapping plus (EQM ) MAE (mm) 4.0 4.0 4.0 4.0 4.6 4.2 RMSE (mm) 7.2 7.2 7.1 7.2 6.9 8.1 SS (unitless) 0.1 0.1 0.1 0.1 0.2 −0.2 R (unitless) 0.4 0.4 0.4 0.4 0.4 0.3 MAE, RMSE, SS, and R, are mean absolute error, root mean square error, skill score, and Person’s correlation coefficients, respectively. 2400 2400 2200 2200 2000 2000 1800 1800 1600 1600 1400 1400 1200 1200 1000 1000 800 800 600 600 OBS CCW MLR OBS CCW2 MLR2 SAM IDW EQM SAM2 IDW2 EQM2 NRM NRM2 (a) (b) 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). and R (0.75). &is showed that the gap-filling techniques increase of failure (percent of missing data) and has better have better performance in meteorological stations located performance when the distance between stations is short. at a higher altitude than those at lower altitudes. &is is because the meteorological stations located in higher ele- 5. Conclusion vations obtain more rainfall in a better pattern (better data statistics) and those located in lower altitudes received er- &e performances of seven gap-filling techniques in esti- ratic rainfall. &e preference to use any of the tested gap- mating the daily observed rainfall data in five meteorological filling techniques has to consider the performances of each stations of Wolaita Zone and the surrounding were tested in technique in each station. In general, MLR without EQM this study. &e techniques were tested against the four widely can be suggested for use in the study area. It is in agreement used evaluation criteria such as mean absolute error (MAE), with the study [69] indicating that the precision of MLR in root mean square error (RMSE), skill score (SS), and estimating the observed rainfall is less affected by the Pearson’s correlation coefficients (R). MLR fulfilled three of Annual Rainfall (mm) Annual Rainfall (mm) 2016 Advances in Meteorology 13 [2] L. M. 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Evaluation of Seven Gap-Filling Techniques for Daily Station-Based Rainfall Datasets in South Ethiopia

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Hindawi Advances in Meteorology Volume 2021, Article ID 9657460, 15 pages https://doi.org/10.1155/2021/9657460 Research Article Evaluation of Seven Gap-Filling Techniques for Daily Station-Based Rainfall Datasets in South Ethiopia 1,2 1 1 3 4 Alefu Chinasho , Bobe Bedadi, Tesfaye Lemma, Tamado Tana, Tilahun Hordofa, and Bisrat Elias 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 Correspondence should be addressed to Alefu Chinasho; chinalefu11@gmail.com Received 5 June 2021; Revised 21 July 2021; Accepted 13 August 2021; Published 19 August 2021 Academic Editor: Stefano Federico Copyright © 2021 Alefu Chinasho et al. &is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Meteorological stations, mainly located in developing countries, have gigantic missing values in the climate dataset (rainfall and temperature). Ignoring the missing values from analyses has been used as a technique to manage it. However, it leads to partial and biased results in data analyses. Instead, filling the data gaps using the reference datasets is a better and widely used approach. &us, this study was initiated to evaluate the seven gap-filling techniques in daily rainfall datasets in five meteorological stations of Wolaita Zone and the surroundings in South Ethiopia. &e considered gap-filling techniques in this study were simple arithmetic means (SAM), normal ratio method (NRM), correlation coefficient weighing (CCW), inverse distance weighting (IDW), multiple linear regression (MLR), empirical quantile mapping (EQM), and empirical quantile mapping plus (EQM ). &e techniques were preferred because of their computational simplicity and appreciable accuracies. &eir performance was evaluated against mean absolute error (MAE), root mean square error (RMSE), skill scores (SS), and Pearson’s correlation coefficients (R). &e results indicated that MLR outperformed other techniques in all of the five meteorological stations. It showed the lowest RMSE and the highest SS and R in all stations. Four techniques (SAM, NRM, CCW, and IDW) showed similar performance and were second-ranked in all of the stations with little exceptions in time series. EQM improved (not substantial) the performance levels of gap-filling techniques in some stations. In general, MLR is suggested to fill in the missing values of the daily rainfall time series. However, the second-ranked techniques could also be used depending on the required time series (period) of each station. &e techniques have better performance in stations located in higher altitudes. &e authors expect a substantial contribution of this paper to the achievement of sustainable development goal thirteen (climate action) through the provision of gap-filling techniques with better accuracy. predominantly caused by the provisional absence of ob- 1. Introduction servers, equipment miscarriage, data archiving, and irregular Rainfall (precipitation) is one of the key inputs in many calibration of devices [4, 5]. Ignoring the missing values disciplines such as climatology (climate variability and from analyses has been used as a technique to manage it change), meteorology (weather conditions), irrigation en- [6–8]. However, it leads to partial (coarse resolution) and gineering (irrigation scheduling), hydrology (water cycle), biased results in data analyses [9–11]. Instead, filling the data and environmental hazard assessment (floods). Despite its gaps using reference datasets such as reanalysis products or overriding uses, the rainfall dataset of meteorological sta- estimates from the surrounding stations are better and tions has gigantic missing values, mainly in developing widely used approaches [12–15]. Ample gap-filling tech- countries [1–3]. Data gaps in rainfall time series are niques have been evaluated and suggested in the literature to 2 Advances in Meteorology globe (Serially Complete Earth) dataset using the global fill in the missing daily rainfall time series at different parts of the world. &e majority of gap-filling techniques are spatial historical climatology network daily (GHCND), a global surface summary of the day (GSOD), and Environment and interpolation methods. Among the spatial interpolation techniques, simple Climate Change Canada (ECCC). In addition, Noh and Ahn arithmetic mean (SAM) was indicated for its best perfor- [39] developed a new gridded rainfall dataset (K-Hydra) mance and computational simplicity in some studies over the Korean peninsula to fill rainfall data gaps, which has [16–18]. But, [19, 20] prioritized inverse distance weighting comparable performance with global precipitation clima- (IDW) over other spatial interpolation techniques. Out- tology project (GPCP), climate prediction center (CPC), performance was also reported for the normal ratio method tropical rainfall measuring mission (TRMM), and Asian precipitation highly resolved observational data integration (NRM) [16, 21, 22], correlation coefficient weighing (CCW) [23], and multiple linear regression (MLR) [24]. Never- towards evaluation (APHRODITE). In Ethiopia, some studies evaluated and suggested dif- theless, Longman et al. [25] specified no statistical differ- ences (similar performance) between five spatial ferent gap-filling techniques for daily rainfall time series. For instance, Boke [40] evaluated five spatial gap-filling tech- interpolation techniques (normal ratio method, linear re- gression, inverse distance weighting, quantile mapping, niques in ten meteorological stations in Ethiopia and sug- and single best estimator) for large gaps. Machine learning gested the nearest neighbor, inverse distance weighting processes such as the artificial neural network (ANN), average, and modified inverse distance weighting average for Kernel approaches, and kriging are also suggested in some the country. Woldesenbet et al. [41] also tested four gap- studies to fill the rainfall data gaps. &e best performance of filling techniques in 38 stations in the upper Blue Nile basin the machine learning process was stated for ANN [26, 27], of Ethiopia in which CCW showed the best performance over NRM, modified NRM, and IDW. Similarly, Armanuos ordinary kriging [28, 29], and Kernel approaches [30]. Besides, Grillakis et al. [31] indicated the acceptable per- et al. [17] assessed twenty-one (21) gap-filling methods in 15 stations and suggested that NRM, MLR, IDW, CCW, and formance of empirical quantile mapping in filling the discontinued daily rainfall data in the Mediterranean island SAM fill in the missing rainfall data in Ethiopia. &e reviewed literature indicates that the performances of gap- of Crete. Combining or modifying the previously existing gap- filling techniques vary between stations, considered evalu- filling techniques is also reported for better performance ation criteria, statistical properties of data [17], and density than using the techniques separately. Teegavarapu et al. [32] and the geometrical organization of the station network [42]. indicated that the linear weight optimization method Yet, to the authors’ best knowledge, none of the reviewed (LWOM) with a single best estimator (SBE) performed literature and no related study covered the meteorological better than SBE only in Florida. Similarly, Kim and stations located in Wolaita Zone and the surroundings. Moreover, the applicability of gap-filling methods is limited Pachepsky [33] concluded that the regression tree (RT) with ANN showed better performance than solely using RT or by many factors including the required computational skill and the percentage of gaps in the data [43]. On the other ANN in the Chesapeake Bay watershed of the USA. Fur- thermore, Khosravi et al. [34] presented better performance hand, Ethiopia is a large country covering about 1,104,300 of the modified geographical coordinate (GC) method than square kilometers [44] in which directly using any of the the previously available methods in 24 station gauges in Iran. suggested techniques for the entire country is not repre- Mart´ınez et al. [35] also showed that the generalization of the sentative and can lead to biased results. So, testing the gap- modified normal ratio with the inverse distance weighting filling techniques at local levels is very important. and the generalization of modified correlation coefficient &us, this study was initiated to evaluate the perfor- with the inverse distance weighting method outperformed mances of seven gap-filling techniques to fill in the missing NRM, NRM weighted with correlation, NRM modified with values of daily rainfall data in the meteorological stations of Wolaita Zone and the surroundings in South Ethiopia. &e IDW, CCW, modified CCW, IDW, modified correlation coefficient with IDW, IDW weighing of NRM with corre- seven selected techniques were simple arithmetic mean (SAM), normal ratio method (NRM), inverse distance lation, and IDW-modified height. Similarly, Rahman et al. [36] indicated that the generalized linear model with gamma weighting (IDW), correlation coefficient weighing (CCW), and Fourier series was outperformed over SAM, NRM, multiple linear regression (MLR), empirical quantile map- CCW, and IDW in estimating the missing daily rainfall ping (EQM), and empirical quantile mapping plus (EQM ). series. &e Gaussian mixture model-based KNN imputation &e techniques were preferred among others due to their showed better performance level than KNN only [37]. computational simplicity, wider application, and compa- Filling the rainfall data gaps using the reanalysis prod- rable performance with other techniques [45]. Performances ucts is also another widely used approach. For example, of the techniques were tested against four evaluation criteria Cordeiro and Blanco [38] indicated that the Climate Haz- such as mean absolute error (MAE), root mean square error ards Group InfraRed Precipitation with Stations (CHIRPS) (RMSE), skill score (SS), and Pearson’s correlation coeffi- product outperformed the tropical rainfall measuring mis- cients. As well, the performance consistency was evaluated sion (TRMM) and Morphing Technique (CMORPH-CPC) on different time scales. in estimating daily rainfall time series in the Amazon region. &e authors of this paper expect momentous contri- Further, Tang et al. [14, 15] filled the data gaps in daily butions of the paper to environmentalists, engineers, cli- rainfall of North America (serially complete NA) and the matologists, agriculturalists, and natural resource Advances in Meteorology 3 management experts facing rainfall data gaps. &e tech- from February and March to December. It ranges between ° ° niques included in this study can be tracked on any other 8.65 C (in Hosana) and 15.4 C (in Areka) (see Table 1). location and their performances can be compared with the findings of this work. Besides, the filled rainfall datasets of 2.2. Methodology. &e methodology of this work trailed the five meteorological stations (Areka, Bele, Boditi, Hosana, following processing steps. First, the data matrixes of five and Shone) are freely available based on requests. Moreover, stations with complete data (excluding the years of data our findings have a substantial contribution to sustainable missing) were prepared. For the gap-filling techniques other development goal (SDG) thirteen (climate action) by pro- than quantile mapping and quantile mapping plus, the viding the filled and summarized rainfall data freely so that datasets of five (all) stations were considered. In the em- the policymakers of the country can use it to understand the pirical quantile mapping (EQM and EQM ), the datasets of climate variability and change in the study area with reduced three stations (one target and two with higher correlation error level. So, it provides imperative information to take coefficients) were used. &e correlation between a target action on climate change adaptation and mitigation mea- station and the surrounding stations is more important than sures. &e rest part of this paper is organized into four proximity (physical distance) of the stations [25]. &en, the sections. Section 2 describes the materials and methods: seven gap-filling techniques were cross-validated using four study area and data description and methodology for gap- evaluation criteria, and the missing values were estimated filling techniques and evaluation criteria. Section 3 presents using the best-performed technique. In the case when there the results of the gap-filling techniques of the missing daily is no data from neighboring stations, the method used by precipitation data in five meteorological stations. Section 4 Ismail and Ibrahim [50], using the mean on the same day discusses and interprets the results. Finally, Section 5 con- and month but at different years, was used to estimate the cludes the findings of this study. missing value on that particular date. &e detailed meth- odology is described in the following paragraphs. 2. Materials and Methods 2.1. Study Area and Data Description. Five meteorological 2.2.1. Simple Arithmetic Mean (SAM). It estimates the stations located in two zones (Wolaita and Hadiya) of missing values in the target station from the surrounding southern nations’ nationalities and people’s regional state of stations by simply taking the average of surrounding stations’ Ethiopia were included in this study (see Figure 1). From the data in the same period of missing value [51]. &is is the five stations, two (Hosana and Shone) are located in Hadiya simplest technique of estimating missing values used when Zone and three stations (Areka, Bele, and Boditi) are located the missing value has less than 10% [52]. It is expressed as in Wolaita Zone. &e five meteorological stations considered 􏽐 V in this study are sufficient and comparable with the four i�1 i (1) V � , stations [46, 47] and six stations [48] of similar studies. &e n stations are located from 6.92 to 7.57 (latitude) and from 37.5 where V is the estimated value of the missing data, V is the o i to 37.95 (longitude) and in the altitudinal ranges of th value of the same variable at the i nearest station, and n is the 1240–2397 meters above sea level (see Table 1). &e observed number of nearest weather stations considered for averaging. daily rainfall and maximum and minimum temperature data of five stations for periods (1987–2017) were obtained from the National Meteorological Agency (NMA) of Ethiopia [49]. 2.2.2. Normal Ratio Method (NRM). It considers the cor- &e stations have huge missing values up to 30.2% in relation coefficients between the target station and the sur- daily rainfall, 29.4% in maximum temperature, and 19.4% in rounding stations. It is recommended for filling in missing minimum temperature (see Table 1). Besides, Bele and values if more than 10% of the data is missing [52]. It gives Shone stations did not have the dataset for maximum and weight to the data of surrounding stations based on their minimum temperature in the study period. So, the two correlation with the target station. It is expressed as follows: stations were not considered in analyses of maximum and 􏽐 W V i�1 i i minimum temperature (see Table 1). &e rainfall datasets of V � , (2) o n 􏽐 W five stations have a bimodal pattern (two peaks in the year) i�1 even though the months of obtaining peak values slightly where V is the estimated value, W depicts the weight of the o i vary from station to station (see Figure 2, presented in bar th i surrounding weather station, and V is the value of the charts). Two peak values of rainfall were observed in April th same variable at the i station. &e weight of the sur- and August in Areka and Hosana stations, April and July in rounding station is calculated using the following equation: Shone, May and August in Boditi, and May and July in Bele stations. &e study area received an annual rainfall between n − 2 W � r 􏼠 􏼡, (3) i 2 1,212 (in Hosana) and 1,561 mm (in Shone). Besides, the 1 − r maximum temperature has a bimodal distribution pattern th (see Figure 2: presented in lines). &e mean monthly where W is the weight of the i station, r corresponds to the th maximum temperature varies between 19.34 C (in Hosana) correlation coefficient between the target station and the i and 29.5 C (in Areka) (see Table 1). &e minimum tem- surrounding station, and n is the number of points used to perature of the area has a continuously decreasing trend calculate the correlation coefficient. 4 Advances in Meteorology 240000 280000 320000 360000 400000 440000 850000 850000 820000 820000 790000 790000 760000 760000 730000 730000 Scale: 1:1,200,000 240000 280000 320000 360000 400000 440000 Stations National Selected Zones Selected Zones in SNNPRS Figure 1: Location map of five meteorological stations in Wolaita Zone and the surroundings. SNNPRS is southern nations’ nationalities’ and peoples’ regional state of Ethiopia. Table 1: Description of five meteorological stations in Wolaita Zone and the surroundings. Stations Geographic information Areka Bele Boditi Hosana Shone Latitude (degree) 7.07 6.92 6.95 7.57 7.13 Longitude (degree) 37.7 37.53 37.96 37.85 37.95 Altitude (meter) 1804 1240 2043 2307 1959 Rainfall Data coverage 1988/2017 1987–2018 1987–2018 1987–2018 1987–2018 Missing data (%) 30.2 21.5 4.5 2.7 8.4 Monthly total value 1536.84 1250.16 1264.66 1212.34 1560.58 Minimum value 29.54 28.74 34.72 11.92 37.06 Maximum value 209.1 174.44 182.08 165.66 235.94 Mean value 128.07 104.18 105.4 101.03 130.05 Standard deviation 68.7 61.13 53.94 55.1 68.63 Maximum temperature Data coverage 1992–2017 NA 1987–2018 1987–2018 NA Missing data (%) 29.4 NA 4.6 14.8 NA Minimum value 22.2 NA 21 19.34 NA Maximum value 29.5 NA 28.4 25.6 NA Advances in Meteorology 5 Table 1: Continued. Stations Geographic information Areka Bele Boditi Hosana Shone Mean value 25.7 NA 25 22.7 NA Standard deviation 2.5 NA 2.5 2.14 NA Minimum temperature Data coverage 1992–2017 NA 1987–2018 1987–2018 NA Missing data (%) 19.36 NA 4.7 12.5 NA Minimum value 12.95 NA 11.99 8.65 NA Maximum value 15.44 NA 14.29 12.03 NA Mean value 14.14 NA 13.28 10.81 NA Standard deviation 0.72 NA 0.75 0.95 NA NA is data not available. 250.0 200.0 150.0 100.0 50.0 0.0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec RF_Areka RF_Shone Tmin_Areka RF_Hosana Tmax_Areka Tmin_Boditi RF_Bele Tmax_Boditi Tmin_Hosana RF_Boditi Tmax_Hosana Figure 2: Mean monthly annual rainfall and temperature (maximum and minimum) patterns in Wolaita Zone and the surroundings. RF is ° ° the total rainfall (mm), Tmax is the mean maximum temperature ( C), and Tmin is the mean minimum temperature ( C). 2.2.3. Inverse Distance Weighting (IDW). It is the most where V is the estimate obtained for missing value, V is the o i th th commonly used technique for estimating the missing values observed value at the i station, d is the i surrounding of daily rainfall [53]. It assumes that the closer the sur- station distance, and n is the number of stations used. &e rounding stations to the target station, the better the esti- distance between the target station and the surrounding mation of missing values and the lower the error in stations is calculated using the Pythagoras formula. estimation or the better the accuracy. It is calculated using 􏽱������������������� 2 2 (5) the following equation d � X − X􏼁 + Y − Y􏼁 , i a i a i 􏽐 V /d i�1 i i where d is the distance between the target station and the V � , (4) i o n th 􏽐 1/d􏼁 i�1 surrounding i station, X and X are the longitudes, and Y a i a Rainfall (mm) and Temperature (°C) 6 Advances in Meteorology th th and Y are the latitudes of the target and the i surrounding where Qm (t) is the t estimated daily data at the target −1 stations, respectively. &en, the values in degrees are mul- station, Fo is the inverse cumulative distribution function tiplied by 111 to convert them to kilometers. (CDF) of the available data at the target station, Qs (t) is the th t daily data at the neighboring station, and Fs is the CDF of the daily data at the neighboring station. 2.2.4. Correlation Coefficient Weighing (CCW). In this ap- proach, distance is replaced by Pearson’s correlation coef- ficients [54]. It assures that the datasets of surrounding 2.2.7. Empirical Quantile Mapping Plus (EQM ). In this stations having a better positive correlation with that of the study, we used the name “empirical quantile mapping plus target station give better estimates of missing values in target (EQM )” to refer to the empirical quantile mapping ap- stations than that of less correlated ones. &us, Pearson’s plied to the outputs (values estimated by all six tech- correlation coefficients between rainfall data of five mete- niques). &e study [31] obtained a better result (reduced orological stations were analyzed, and the missing values in mean absolute error) after applying quantile mapping on target stations were determined using the following the outputs generated by other techniques. &us, we ap- equation: plied it to evaluate its performance on the outputs obtained by other techniques. First, the data matrix was made be- 􏽐 r V i�1 i i tween the observed, an average of observed data, and the V � , (6) o n 􏽐 r i�1 outputs of SAM, NRM, CCW, MLR, IDW, and EQM. &en, the data matrix was refed to R-software for the where V is the missing value of the target station, r is the th empirical quantile mapping process. Finally, the output correlation coefficient of the i surrounding station, and V is th was subjected to cross-validation analysis against preset the value of the same variable in the i surrounding station. criteria. 2.2.5. Multiple Linear Regression (MLR). It was carried out by considering the linear significant relationship between 2.3. Performance Evaluation of Gap-Filling Techniques. the observed values of the target station and the surrounding Cross-validation was assessed by comparing the observed data and the data estimated by different gap-filling tech- stations [55]. &e dataset of the target station was considered as a dependent variable and the surrounding stations’ niques. It was used to evaluate the quality (performance) of different gap-filling techniques based on four commonly datasets were considered as independent variables. Ac- cordingly, the multiple linear regressions were carried out used statistical validation (evaluation) criteria. &e con- sidered evaluation criteria are mean absolute error (MAE), for five stations. &en, the missing values in the target station were filled using the intercept and the coefficients of the root mean square error (RMSE), skill score (SS), and variables were expressed as follows: Pearson’s correlation coefficients (R). Similar evaluation criteria were considered in identical studies conducted by [60–62]. &e best-performing technique was selected based V � a + 􏽘 a V􏼁 , (7) o 0 i i i�1 on cross-checking its performances under many criteria. &e gap-filling techniques were evaluated as the best where V is the estimated value, a , a , . . . , a are regression o 0 i n performing under three different conditions. &e first coefficients, and V is the value of the same parameter at the condition (default) to decide the gap-filling techniques as th i weather station. 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 2.2.6. Empirical Quantile Mapping (EQM). It is a very coefficient (R). Next, when the estimation technique ful- common technique used to downscale the global circulation filled three evaluation criteria out of the four. &e last model (GCM) outputs of rainfall to the regional and local condition was when the estimation technique fulfilled two levels [56, 57]. It requires three elements (observed, his- evaluation criteria and showed at least equal performance torical, and projected datasets) for analysis. However, very level with other good performing techniques at least in one few studies used this technique to estimate the missing daily criterion. On the other hand, no gap-filling technique was rainfall of the target station [58, 59]. We used the observed decided as best performing under conditions other than data of the target station and that of two stations having a these three. A similar procedure was followed to evaluate better correlation with the target station data and carried out whether the application of empirical quantile mapping plus EQM using R-software. QM is expressed as follows: (EQM ) improved the performances of gap-filling tech- −1 Qm(t) � Fo [Fs[Qs(t)]], (8) niques or not. Advances in Meteorology 7 Vobs − Vest 􏽐 􏼁 i�1 i i MAE � , 􏽳����������������� � n 2 􏽐 Vobs − Vest 􏼁 i�1 i i RMSE � , MSE(Vest, Vobs) SS(Vest, Vobs and AVobs) � 1 − , MSE(Vavg, Vobs) (9) n 2 􏽐 Vest − Vobs 􏼁 i i i�1 MSE(Vest, Vobs) � , 􏽐 Vavg − Vobs 􏼁 i�1 i MSE(AVobs, Vobs) � , 􏽐 Vobs − AVobs􏼁∗ Vest − AVest􏼁 1 i i 􏽱��������������������������������������� R � , 2 2 n n 􏽐 Vobs − AVobs ∗ 􏽐 Vest − AVest 􏼁 􏼁 i�1 i i�1 i th where Vest and Vobs are the estimated and observed i (yellow line) was outperformed in estimating the observed i i values, respectively, AVobs and AVest are the average of annual total rainfall (red line) of Bele station in all the years observed and estimated values, respectively, and n is the (1988–2017) (see Table 3 and Figure 4(a)). Besides, no other number of data points. MAE, RMSE, SS, and R are the mean techniques obtained the positive value of the skill score absolute error, root mean squared error, skill score, and except MLR. Except for EQM, the rest of the gap-filling Pearson’s correlation coefficient, respectively. techniques showed similar performance (no significant variation in their statistics) and ranked second. Similarly, they (except for EQM) showed comparable performance 3. Results with MLR in estimating the annual total rainfall of Bele 3.1. Performances of Gap-Filling Techniques in the Areka station up to the year 2002 (see Figure 4(a)). &us, these techniques could be used if the data required are up to the Meteorological Station. &e multiple linear regression year 2002 only; otherwise, MLR is suggested to fill rainfall (MLR) gap-filling technique outperformed other techniques data gaps in Bele station. But, the performance levels of all under the root mean square error (RMSE), skill scores (SS), gap-filling techniques became poorer after the application of and Pearson’s correlation coefficient (R) evaluation criteria empirical quantile mapping plus (see Figure 4(b)). All of the in Areka station (see Table 2). It showed the lowest RMSE techniques overestimated the annual total rainfall of Bele (7.75 mm) and the highest SS (0.16) and R (0.29). Its per- + + station after EQM . &us, using EQM is not advisable to fill formance of estimating observed rainfall was appreciable up the rainfall data gaps in Bele station. 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 3.3. Performances of Gap-Filling Techniques in Boditi-School (EQM), the rest of the gap-filling methods showed com- Station. Under the three evaluation criteria (RMSE, SS, and parable (similar) and second-ranked performance. It is only R), MLR showed the best performance in Boditi-School EQM that showed the negative (poor value) of skill scores station. &e lowest RMSE (7.01 mm) and the highest SS (SS � −0.31). &e performance levels of gap-filling tech- (0.2) and R (0.45) were observed in MLR (see Table 4). &e niques became poor after empirical quantile mapping plus: yellow line of MLR showed a consistent performance in all the techniques overestimated the observed values (see estimating the observed annual total rainfall (OBS: red line) Table 2 and Figure 3(b)). Despite its poor performance after throughout the estimation period except for (2006-2007 2010, no other gap-filling techniques (including EQM ) have and 2014-2015) in Boditi-School station (see Figure 5(a)). comparable performance in Areka station. So, MLR gap- &e remaining techniques overestimated the observed filling technique can be used to fill rainfall data gaps in Areka annual total rainfall between 1992 and 2000 (see station. Figure 5(a)). &e poorest performance was observed in EQM (the only technique with the negative values of SS). 3.2. Performances of Gap-Filling Techniques in Bele Station. Except for MLR and EQM, the performance levels of all As in Areka station, MLR outperformed other techniques by techniques were improved after applying EQM up to the considering three evaluation criteria in Bele station (RMSE, year 2005 and became poorer after 2005 (see Figure 5(b). SS, and R) (see Table 3). &e lowest RMSE (7.43 mm) and the Due to the limited improvement in the performance levels highest SS (0.11) and R (0.33) values were observed in MLR. of gap-filling techniques, EQM is not suggested for use in Except for the periods 1988–1991 and 2004–2009, MLR Boditi-School station. 8 Advances in Meteorology Table 2: Performance evaluation results of gap-filling techniques in Areka station before and after empirical quantile mapping plus (EQM ). Gap-filling techniques Performance evaluation criteria SAM NRM CCW IDW MLR EQM Before empirical quantile mapping plus MAE (mm) 4.16 4.14 4.15 4.21 4.67 5.40 RMSE (mm) 7.96 7.98 7.96 8.04 7.75 9.70 SS (unitless) 0.12 0.11 0.12 0.10 0.16 −0.31 R (unitless) 0.29 0.29 0.29 0.29 0.29 0.22 After empirical quantile mapping plus (EQM ) MAE (mm) 5.01 4.98 5.00 5.06 5.74 6.29 RMSE (mm) 8.11 8.12 8.10 8.21 7.99 10.08 SS (unitless) 0.08 0.08 0.09 0.06 0.11 −0.42 R (unitless) 0.29 0.29 0.29 0.30 0.27 0.22 MAE, RMSE, SS, and R are mean absolute error, root mean square error, skill score, and Person’s correlation coefficients, respectively. 2000 2400 1200 1400 400 400 OBS CCW MLR OBS CCW2 MLR2 SAM IDW EQM SAM2 IDW2 EQM2 NRM NRM2 (a) (b) 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). 3.4. Performances of Gap-Filling Techniques in Hosana considered evaluation criteria (see Table 5). &e perfor- Station. &e outperformance of MLR was observed under mance levels of four techniques (SAM2, NRM2, CCW2, and IDW2) were improved up to the year 2001 (see all (MAE, RMSE, SS, and R) evaluation criteria in Hosana station (see Table 5). MLR has the lowest MAE (3.37 mm) Figure 6(b)). &e poorest performance was observed in and RMSE (5.69 mm) and the highest SS (0.37) and R EQM (the only technique with a negative SS value) both (0.69). Its performance in estimating the observed daily before and after EQM (underestimated the observed rainfall data was consistent with time up to 2010 and rainfall). EQM did not improve the values of a Person’s decreased after 2010 (see Figure 6(a)). However, it showed correlation coefficient (R) in all techniques. Due to the poorer performance after empirical quantile mapping plus absence of weighty improvements in performance levels of (see Figure 6(b)). Except for EQM, the rest of the gap-filling gap-filling techniques after EQM , its application is not techniques showed similar performance under all of the suggested in Hosana station. Annual Rainfall (mm) Annual Rainfall (mm) 2016 Advances in Meteorology 9 Table 3: Performance evaluation results of gap-filling techniques in Bele station before and after empirical quantile mapping plus. Gap-filling techniques Performance evaluation criteria SAM NRM CCW IDW MLR EQM Before empirical quantile mapping plus MAE (mm) 4.38 4.37 4.37 4.47 4.47 5.21 RMSE (mm) 7.91 7.95 7.92 8.13 7.43 10.18 SS (unitless) −0.01 −0.02 −0.02 −0.07 0.11 −0.68 R (unitless) 0.33 0.33 0.33 0.32 0.33 0.23 After empirical quantile mapping plus (EQM ) MAE (mm) 4.51 4.48 4.49 4.59 4.75 5.33 RMSE (mm) 8.03 8.06 8.03 8.25 7.44 10.25 SS (unitless) −0.04 −0.05 −0.04 −0.10 0.11 −0.70 R (unitless) 0.33 0.33 0.33 0.32 0.33 0.24 MAE, RMSE, SS, and R, are mean absolute error, root mean square error, skill score, and Person’s correlation coefficients, respectively. OBS CCW2 MLR2 OBS CCW MLR SAM2 IDW2 EQM2 SAM IDW EQM NRM2 NRM (a) (b) 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). 3.5. Performances of Gap-Filling Techniques in Shone Station. observed data between 1992 and 1998 in Shone station (see MLR also outperformed other techniques in estimating the Figures 7(a) and 7(b)). When compared with other stations, all of the gap-filling techniques showed the poorest per- annual total rainfall of Shone station (see Table 6). However, it showed poor performance between 1992 and 1998 (see formance in Shone station. Figure 7(a)), which is expressed in its highest value of MAE (4.4 mm). Except for EQM, the rest of the gap-filling 4. Discussion techniques showed similar performance in Shone station. &e performance levels of gap-filling techniques were not Evaluating the performances of gap-filling techniques at improved after the application of empirical quantile map- station levels has paramount benefits. MLR outperformed ping plus (Figure 7(b)). All of the considered techniques other techniques in all of the considered (five) meteorological failed to catch the highest and lowest rainfall values of stations in Wolaita Zone and the surroundings. &e Annual Rainfall (mm) Annual Rainfall (mm) 2016 10 Advances in Meteorology Table 4: &e performance evaluation result of gap-filling techniques in Boditi-School station before and after empirical quantile mapping plus. Gap-filling techniques Performance evaluation criteria SAM NRM CCW IDW MLR EQM Before empirical quantile mapping plus MAE (mm) 3.82 3.84 3.83 3.89 3.83 4.11 RMSE (mm) 7.22 7.23 7.21 7.33 7.01 8.65 SS (unitless) 0.15 0.15 0.15 0.13 0.20 −0.22 R (unitless) 0.44 0.45 0.45 0.43 0.45 0.31 After empirical quantile mapping plus (EQM ) MAE (mm) 3.39 3.39 3.38 3.44 3.24 3.84 RMSE (mm) 7.14 7.13 7.13 7.23 7.17 8.48 SS (unitless) 0.17 0.17 0.17 0.15 0.16 −0.17 R (unitless) 0.44 0.44 0.44 0.43 0.45 0.30 MAE, RMSE, SS, and R are mean absolute error, root mean square error, skill score, and Person’s correlation coefficients, respectively. OBS CCW MLR OBS CCW2 MLR2 SAM IDW EQM SAM2 IDW2 EQM2 NRM NRM2 (a) (b) Figure 5: 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 Boditi-School station. &e performance of gap-filling methods after EQM is expressed with an extension of number 2 (e.g., SAM to SAM2). outperformance of MLR in estimating the observed rainfall rainfall [65, 66], yet MLR considers the linear relationships data was also observed in meteorological stations of southern between the observed and estimated values. Besides, MLR Iran [63] and South Central Chile [64]. In the study area, MLR increased the number of rainy days (i.e., no zero was obtained estimates the daily observed rainfall with the mean absolute in estimates of MLR) which limited its performance. &e poor error of 4.67 mm in Areka, 4.47 mm in Bele, 3.83 mm in performance of MLR in estimating the observed daily rainfall Boditi-School, 3.37 mm in Hosana, and 4.4 mm in Shone dataset was observed in China under MAE and RMSE stations. In some years in the considered period (1988–2017), evaluation criteria [67]. Teegavarapu [68] also appreciated the MLR showed poorer performances like failure to catch ex- performance of MLR in estimating the daily rainfall of treme values. &e inconsistency of the MLR performance is Kentucky in the USA but did not suggest using it due to its associated with the conditional (inconsistent) process of negative correlation coefficient. Annual Rainfall (mm) Annual Rainfall (mm) 2016 Advances in Meteorology 11 Table 5: Performance evaluation results of gap-filling techniques in Hosana station before and after empirical quantile mapping plus. Gap-filling techniques Performance evaluation criteria SAM NRM CCW IDW MLR EQM Before empirical quantile mapping plus MAE (mm) 3.85 3.84 3.84 3.86 3.37 3.89 RMSE (mm) 7.14 7.14 7.14 7.16 5.69 8.37 SS (unitless) 0.01 0.01 0.01 0.00 0.37 −0.36 R (unitless) 0.38 0.38 0.38 0.38 0.69 0.28 After empirical quantile mapping plus (EQM ) MAE (mm) 3.48 3.47 3.47 3.49 3.16 3.64 RMSE (mm) 6.86 6.86 6.86 6.87 6.00 8.00 SS (unitless) 0.08 0.08 0.08 0.08 0.30 −0.25 R (unitless) 0.37 0.37 0.37 0.37 0.69 0.26 MAE, RMSE, SS, and R are mean absolute error, root mean square error, skill score, and Person’s correlation coefficients, respectively. 1800 1700 1600 1500 1200 1100 1000 900 800 700 600 500 OBS CCW MLR OBS CCW2 MLR2 SAM IDW EQM SAM2 IDW2 EQM2 NRM NRM2 (a) (b) 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). With little variations between stations, four of the gap- filling techniques between stations. &is is because all sta- filling techniques (SAM, NRM, CCW, and IDW) ranked tions have a similar rainfall pattern of the bimodal (peak and second in estimating the observed rainfall in the Wolaita valley). Besides, their statistics of variation between the Zone and the surroundings. Empirical quantile mapping observed and mean values (standard deviation) between showed the poorest performance in all of the five stations. It stations are comparable (53.94–68.7 mm) (see Table 1). is the only technique that showed the negative skill scores To determine the relationships between the altitude of values in all stations. Empirical quantile mapping plus meteorological stations and performance levels of the (EQM ) improved the performance levels of some gap- techniques, Pearson’s correlation was analyzed. &e results filling techniques, though the improvement is not sub- indicated that there was a strong negative correlation be- stantial. However, it did not improve the performance level tween altitude and MAE (−0.91) and between altitude and of MLR in any of the five stations. &ere was a statistically RMSE (−0.72). Besides, a strong positive correlation was nonsignificant difference in the relative performance of gap- obtained between altitude and SS (0.82) and between altitude Annual Rainfall (mm) Annual Rainfall (mm) 2016 12 Advances in Meteorology Table 6: Performance evaluation results of gap-filling techniques in Shone station before and after empirical quantile mapping plus. Gap-filling techniques Performance evaluation criteria SAM NRM CCW IDW MLR EQM Before empirical quantile mapping plus MAE (mm) 4.0 4.0 4.0 4.0 4.4 4.3 RMSE (mm) 7.3 7.3 7.3 7.4 6.9 8.5 SS (unitless) 0.1 0.1 0.1 0.0 0.2 −0.3 R (unitless) 0.4 0.4 0.4 0.4 0.4 0.3 After empirical quantile mapping plus (EQM ) MAE (mm) 4.0 4.0 4.0 4.0 4.6 4.2 RMSE (mm) 7.2 7.2 7.1 7.2 6.9 8.1 SS (unitless) 0.1 0.1 0.1 0.1 0.2 −0.2 R (unitless) 0.4 0.4 0.4 0.4 0.4 0.3 MAE, RMSE, SS, and R, are mean absolute error, root mean square error, skill score, and Person’s correlation coefficients, respectively. 2400 2400 2200 2200 2000 2000 1800 1800 1600 1600 1400 1400 1200 1200 1000 1000 800 800 600 600 OBS CCW MLR OBS CCW2 MLR2 SAM IDW EQM SAM2 IDW2 EQM2 NRM NRM2 (a) (b) 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). and R (0.75). &is showed that the gap-filling techniques increase of failure (percent of missing data) and has better have better performance in meteorological stations located performance when the distance between stations is short. at a higher altitude than those at lower altitudes. &is is because the meteorological stations located in higher ele- 5. Conclusion vations obtain more rainfall in a better pattern (better data statistics) and those located in lower altitudes received er- &e performances of seven gap-filling techniques in esti- ratic rainfall. &e preference to use any of the tested gap- mating the daily observed rainfall data in five meteorological filling techniques has to consider the performances of each stations of Wolaita Zone and the surrounding were tested in technique in each station. In general, MLR without EQM this study. &e techniques were tested against the four widely can be suggested for use in the study area. It is in agreement used evaluation criteria such as mean absolute error (MAE), with the study [69] indicating that the precision of MLR in root mean square error (RMSE), skill score (SS), and estimating the observed rainfall is less affected by the Pearson’s correlation coefficients (R). MLR fulfilled three of Annual Rainfall (mm) Annual Rainfall (mm) 2016 Advances in Meteorology 13 [2] L. M. 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Advances in MeteorologyHindawi Publishing Corporation

Published: Aug 19, 2021

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