Abstract
Climate change increases the possibility in varying rainfall and temperature that needs a detail study to estimate flood frequency under changing climate for the Woybo catchment in the Omo River basin of Ethiopia. The impact on flood frequency was evaluated using multiple climate models under RCP4.5 and RCP8.5 emission scenarios for 2020s, 2050s, and 2080s compared to 1976–2005. Hydrologic Engineering Center of Hydrologic Modeling System (HEC-HMS) was used to simulate streamflow after sensitivity analysis, calibration, and validation of the model for the catchment. Flood frequency analysis was initiated after discharge through a longer section followed by frequency analysis by partial duration series approach which provides a better result even though threshold selection is cumbersome. The results from the nonparametric Mann–Kendall test illustrate a slight increase in annual rainfall. The projected flow is expected to increase in autumn, summer, and annually by 8.34, 13.54, and 5.02% in the 2050s and 12.20, 18.06, and 11.87% in 2080s, respectively, under RCP4.5, while it is likely to increase in summer and annually by 15.66 and 5.82% in 2050s and 10.55 and 29.51% in 2080s, respectively, under RCP8.5. Flood frequency was analyzed by using Gumbel’s method. The flood magnitude predicts a positive change for 10, 50, 100, 200, 500, and 1000 years recurrent periods under both scenarios. This research paves way to reduce the negative impacts of flooding and plays a vital role in providing estimates of recurrence floods which are used in designing roads, dams, and bridges for sustainable water resources management.
1. Introduction
Frequent climate change across Ethiopia has a tremendous effect on the natural environment [1]. It has been widely accepted that climate change is imminent and further changes is inevitable [2]. The long-term continuity of increase or decrease in climatic variables [3] has altered the hydrological regime, and has strong implications on extreme events [4]. Climate is a contributing factor to flood hazard by raising precipitation relative to the average annual rainfall [5].
Flood frequency information is commonly applied to controlling land use and settlement on flood prone areas besides other complicacies [6] due to recurrent changing climate [7]. Climate change effect on flood frequency is due to heavy rainfall and temperature [8] causing changes in timing, regional patterns, and intensity of precipitation events, as well as the number of days with heavy and intense precipitation occurrences. The potential for increased flooding due to climate change would be exacerbated by erosion associated with deforestation and overgrazing which leads to increased surface runoff and severity of flooding [9]. Climate change is expected to increase both the magnitude and frequency of extreme precipitation events causing repeated river flooding [10]. Extreme rainfall event is one of the most significant aspects of climate change. The increase in frequency and intensity as well as runoff events may illustrate major impacts on natural and human-induced systems in terms of increased frequency and severity of floods, flood magnitude, and streamflow volume which is most prevalent in most of the parts of the world.
Ethiopia’s topographic and climatic characteristics have made the country vulnerable to high floods that resulted in destruction and damages to economic, livelihoods, and infrastructure [11]. Floods vary greatly depending on the location and extent [12] influencing communities on economic and environmental values. The impact of different climate change scenarios is projected at a global scale; the exact type and magnitude of the impact at a small watershed scale remain unexploited in most parts of the country. Therefore, identifying localized impact of climate change at a watershed level and quantitative estimates of hydrological effects of climate change has become a challenge. This also gives an opportunity to define the degree of vulnerability of local water resources to climate change and plan appropriate adaptation measures in due course of time [13].
The study assesses the climate change pattern and its impacts on flood frequency in Woybo River catchment. The rainfall–runoff model was used to generate the future streamflow for the projected climate. Selecting a particular model structure for a specific application is one of the challenges for the user. Considering models which are readily available and whose investment of time and money appeared worthwhile are more favorable meeting the aims of a particular project. A list of assumptions was made by the model and assumptions were checked for the response of the catchment. This assessment will be a relative one, or at best, a screen to reject those models that are based on incorrect representations of the catchment processes [14].
Hydrologic Engineering Center Hydrological Modeling System (HEC-HMS) is the US Army Corps of Engineers’ hydrologic system computer program developed by the Hydrological Engineering Center. It is a conceptual semidistributed model designed to simulate the rainfall–runoff processes. It can be applied to analyze urban flooding, flood frequency, flood warning system planning, reservoir spillway capacity, and stream restoration [15]. The model can help to save time and money in gaining the runoff data rather than measurement of runoff in the watershed. The HEC-HMS model is a simple and powerful tool for simulation [16]. It is used because of its compatibility with GIS software (Geo-HMS extension). The model is used widely across the globe to simulate runoff to a wide variety of watersheds and evaluate basin response by partially representing spatial heterogeneity by dividing the basin into several subbasins, depending upon the resolution of available input data [17]. HEC-HMS model has been used successfully in different parts of the world, including Ethiopia, for catchment modeling [18]. The model simplifies the actual runoff process, without considering the interaction between the river, the ground, and underground aquifers, and it merges the overland flow and interflow into direct runoff. The model has the advantages of comprehensive consideration of climate and underlying conditions and can choose different calculation methods according to different catchments, data situation, or calculation requirements, and it has a wide range of adaptability [19].
Its simplicity, wide acceptance, applicability, capability, and suitability for flood forecasting in catchments as well as a continuous simulation of runoff were tested [16].
Effective planning and design of hydraulic structures require good estimates of the behavior of extreme hydrological events to protect the structure from destruction, economic loss, environmental damage, as well as loss of life [20]. The correlation between discharge and return period is distinctive for each river discharge gauging location. The traditional annual maximum (AM) series approach is still the most favorable method for flood frequency analysis in many developing countries, including Ethiopia. AM model is demarcated by the maximum peak flow of each year to restrict the loss of information [21]. Some peaks that were not annual maximum series, but are still relatively high, are not considered in annual maximum analyses. Even if some very low discharge values can be part of the AM series model though the sample size is very limited. An alternative to the AM method is the peaks-over-threshold (POT) approach (Partial duration series approach). The POT sample is defined by all peak values that lie above a certain truncation level known as the threshold or base level. Major difficulties in using the POT method are assuring the independence of the data series and choosing an appropriate threshold value. Flood frequency analysis based on a POT flood flow with the selected probability distribution is the best way to evaluate flood frequency under changing climate [22]. This study focuses on the current and future flood frequency assessments because they are sensitive flood-related issues in the Woybo catchment.
Estimates of future flood frequency changes in the area have so far been highly uncertain, and evaluations using climate models under representative concentration pathways emission scenario assessments are quite limited. Flood frequency-related problems, especially the variation of design floods under influence of climate change has been of great concern to hydrologists in recent times [23]. However, research on the magnitude and frequency of devastating flood of Woybo catchment is presently not reported. Due to these facts, this paper attempts to assess the flood frequency under changing climate using multiple climate models based on POT approach.
It is important to investigate the trends of the historical climatic variables generating and detecting streamflow change for 2020s, 2050s, and 2080s using the selected HEC-HMS Rainfall-Runoff model relative to baseline period (1976–2005) and analyzing the flood frequency using projected streamflow against baseline flood frequency to manage water resources as well as related problems.
2. Materials and Methods
2.1. Area under Study
Woybo River is one of the tributaries of the Omo River Basin flowing in the southwest of Ethiopia. The basin is located between 6°55′20″ N to 7°2′40″N latitude and 37°51′40″ to 37°31′0″E longitudes (Figure 1). The study area has tropical climate regime with a catchment area of 533.65 km2. Precipitation in the catchment has strong seasonal and elevation variability. The wet season extends from April to October with July and August as the wettest months. Rainfall distribution is largely controlled by the south–north movement of the Inter Tropical Convergence Zone. The maximum and minimum average temperature varies between 19.67°C to 21.83°C and 16.19°C to 18.71°C, respectively [24].
The subbasin receives an average annual rainfall of 1377.74 mm depicting a high spatial and temporal variation of rainfall. The drainage network of Woybo River catchment was extracted from Digital Elevation Model (DEM). The catchment comprising of third order with a drainage density of 0.45 km/km2 consists of 23 streams extending 148.9 km length, having a 1944 km longest flow path and a bifurcation ratio of 0.96.
The agricultural land, forest land, cultivated land, grassland, and wood land contribute 82.54, 10.09, 6.19, 1.16 and 0.02, respectively, of the total land mass (Figure 2(a)) throughout the region, whereas the major soil types in Woybo River catchment were dystric fluvisols, pellic vertisols, chromic luvisols, eutric cambisols, nitosols, and leptosols which are comprising of 55.8, 31.9, 10.54, 1.7, 0.16 and 1.43%, respectively, across the entire study area (Figure 2(b)). Land uses and soil wetness affects surface runoff which generally increases or decreases flood magnitude as well as intensity of flood frequency. Most of time the effect of land use is on runoff depth, runoff coefficient, time of concentration, curve number, and finally on flood magnitude. The forest, shrub, and grasslands which decrease by 4.0, 9.41, and 14.87%, respectively, and agricultural land increasing by 27.06 from 1989 to 2019 as well as average annual interception, groundwater recharge, surface runoff, and actual-evapotranspiration were 36.4, 127.34, 614.95, and 517.59 mm for forest, shrub, grass, and agricultural land, respectively [25].
2.2. Data Collection and Analysis
The meteorological data was collected for a period of 31 years (1987–2017) from the Ethiopian National Meteorological Agency (ENMA) for the stations located in the Woybo catchment. Thirteen years flow data was collected from Ministry of Water, Irrigation, and Energy (MoWIE). The data were checked for its quality, homogeneity, and for its consistency. Inverse distance (reciprocal-distance) weighting method was used for estimation of missing rainfall [26, 27]. The consistency of the individual stations and data was investigated using the double mass curve technique. Independency and statutory of flow data were checked using Wald–Wolfowitz method.
DEM of the watershed was downloaded from Alaska Satellite Facility and extracted by masking the shape file of the Woybo watershed and mosaicking the downloaded DEM grids using ArcGIS 10.2.1 tool. It was used for the development of the basin model component in the HEC-HMS model. Land use/cover map for this study area was obtained from MoWIE Geographic Information System (GIS) Department.
2.3. Climate Data Set
Downscaled rainfall and temperature data for the period 1976–2100 was downloaded from the spatial grid resolutions of all Coordinated Regional Climate Downscaling Experiment (CORDEX) Africa programs for both RCP4.5 (Intermediate emission indicating 4.5 Wm−2) and RCP8.5 (High emission indicating = 8.5 Wm−2) scenarios in the form of Network Common Data Form (NetCDF).
2.4. Selection of Representative Concentrations Pathways (RCPs)
RCPs provide time-dependent projections of atmospheric greenhouse gas concentrations as per the latest climate change scenarios. The main reasons for developing the new RCP scenarios were as a result of Special Report on Emissions Scenarios (SRES) that do not consider climate policy. Latest developments in climate models require detailed information of emissions by source type and to allow consistent usage of scenarios through the collaboration of various disciplines. The new emission scenarios are thus intended to connect work on climate change, impacts, adaptation, and mitigation [28].
RCP8.5 (High Emission) remains consistent with a future having no policy changes to reduce emissions and is characterized by increasing greenhouse gas emissions that lead to high greenhouse gas concentrations over time [29].
RCP 4.5(Intermediate emissions) was developed by Pacific Northwest National Laboratory in the United States. Here radiative forcing is stabilized shortly after 2100, consistent with a future with relatively ambitious emissions reductions [27, 29]. RCP4.5 is considered a more realistic projection scenario [30].
2.5. Selection of Climate Models
Five Regional Climate Models (RCM) models such as Climate Limited-Area Modeling Community Version 4 (CCLM4), Rossby Center Atmospheric Version 4 (RCA4), Regional Atmospheric Climate Model Version22 (RACMO22T), High-Resolution Hamburg Climate Model Version 5 (HIRAM5), and Regional Model (REMO2009) were used. These models were considered on the basis of their performance in the same catchment [24].
2.6. Bias Correction of Climate Data
Climate models data cannot be directly used for impact assessment without bias correction [31]. The raw climate data were corrected in order to produce a better climate projection. Bias correction was applied to compensate the overestimation or underestimation of the mean of downscaled climate data. Quantile Mapping ((QM) which is often called probability mapping) bias correction method was used to achieve a better perseverance of raw climate model for projected changes to temperature and precipitation [31, 32]. This entails in establishing a statistical relationship between observed and model-simulated outputs by substituting observed values for simulated values at the same cumulative density function of the used distribution, depending on the climate variable. Fitting the daily precipitation values of each month to the Gamma distribution corrects for bias in precipitation values greater than zero [33] changing the temperature levels from negative to positive resulting into the normal distribution best fits temperature data:where x is climatic variable; is bias corrected model-simulated data to characterize between the wet and dry day threshold value; is used for day with precipitation greater than 1 mm and is assumed to be a wet day; F is Cumulative Density Function F−1 that is its inverse. (o = observed, m = model, h = historical period, and s = simulation period).
Here, the simulated period can either be a historical or a future period.
Distributions for bias correction of temperature climatic variables were estimated using equation:where x is climatic variable, m = model, h = historical period, and s = simulation period.
The simulated period can either be a historical or a future period.
2.7. Trend Analysis
The trend analysis has been computed by using nonparametric Man–Kendall trend test since the purpose of a trend analysis is to determine the values of a series of data with an increase or decrease to time. This also enables to identify the change in the value from the long-term period of the climate by comparing the trend of the observed with the historical period value numerically. Man–Kendall test has been formulated as a nonparametric test for trend detection and the test statistics distribution [34] for testing nonlinear trend and turning point. It is a nonparametric test since it can avoid the problem caused by data skew and also there is no assumption of a statistical distribution (i.e., normal distribution).
There are two hypotheses to be tested in the Mann–Kendall test. One hypothesis is the null hypothesis H0 which means that there is no trend in concerned time series, while the other is the alternative hypothesis Ha. This alternative hypothesis assumes that there is significant trend in the time series:where,where Yj and Yi represent the data points at the time j and I, respectively, where j > i and n is the last period in the time series. If n > 10, then the statistic (S) is normally distributed with the mean of S as zero, the variance statistic Var (S) by
2.8. HEC-HMS Model Setup
The key input data used for HEC-HMS are rainfall depth, evaporation, observed streamflow, base flow, and different watersheds characteristics obtained from Arc-Hydro tools and HEC-Geo HMS in GIS environment. The process for initial parameter estimation after converting data from geographic to hydrologic data structure in the HEC-Geo HMS is the next step used for configuration of the HEC -HMS model.
HEC-Geo HMS program allows to visualize spatial information, watersheds characteristics, perform spatial analysis, delineate subbasins and streams, construct inputs to hydrologic models, and assist with report preparation working with HEC-Geo HMS through its interfaces, menus, tools, buttons, and context sensitivity online help to appropriately create hydrologic inputs that can be used directly with the HEC-HMS. HEC-Geo HMS creates back ground map files, basin map files, meteorological model files, and a grid cell parameter file which can be used by HEC-HMS to develop a hydrologic model. The basin model file contains hydrologic elements and their hydrologic connectivity. This also includes subbasin areas and other hydrologic parameters that could be estimated using geospatial data.
To assist with estimating hydrologic parameters, HEC-Geo HMS can generate table containing physical characteristics of streams and watersheds [35], the main producers in HEC-Geo HMS to create hydrologic input for HEC-HMS hydrologic modeling are terrain preprocessing, basin processing, stream, and subbasin characteristics, Hydrologic parameter estimation and Hydrological modeling system (HMS) were required for developing HEC- HMS model. GEO-HMS uses spatial analyst tools to convert geographic information in to parameters for each of the basins and flow lines. These parameters are then used to create a HEC-HMS model that can be used within the model program. See the schematization of Woybo catchment in to HEC-HMS model (Figure 3).
The model sensitivity analysis is possibly useful in all stages of the modeling process in model calibration and model validation [36]. Sensitivity analysis is a method to determine which parameters of the model have the greatest impact on the model result. The most sensitive parameter corresponds to greater change in output response. This information is important during model calibration.
For the modeling of short rainfall-runoff events, a detailed accounting of the movement and storage of water through the system is not necessary, for example, Soil Moisture Accounting (SMA) method. The Soil Conservation Service (SCS) curve number method was initially considered for the event modeling, but the loss rate in this method continuously decreases toward zero, and the method is not sensitive to rainfall intensity [37]. Therefore, the event model created for this study used the initial and constant-rate loss method. According to [38], this method has been used successfully in many studies throughout the Ethiopia, is easy to set up and use. In the initial and constant-rate method, the maximum potential rate of rainfall loss or constant-rate CR [mmhr−1] is constant throughout an event. An initial loss IL [mm], represents interception and depression storage. The initial loss parameter defines basin initial condition. If the basin is in a saturated condition, IL will approach zero. If the basin is dry, then IL will represent the maximum rainfall depth that can fall on the basin with no runoff. The constant loss rate is the ultimate infiltration capacity of the soils [38]. Impervious area of the subbasin Ai [%] is also one parameter of an initial and constant loss model.
In the direct runoff component, excess rainfall is transformed into direct runoff. The Clark unit hydrograph [39] is a frequently used technique for modeling direct runoff resulting from individual storm events [40]. The Clark unit hydrograph method represents two key processes in the transformation of excess rainfall to runoff: translation and attenuation. Translation is based on a synthetic time–area histogram and the time of concentration, Tc. The time–area histogram specifies the basin area contributing to flow at the outlet as a function of time. Attenuation is modeled with a linear reservoir. The reservoir represents the aggregated impacts of all basin storage. The parameters of the Clark method are‚ Time of concentration, Tc, [hr], storage coefficient, SC [hr]. Both parameters can be estimated via calibration because observed rainfall and streamflow data are available.
River routing is a process of computing the travel time and attenuation of water flowing in the river. Muskingum routing model was used to route outflow. The parameters in the Muskingum routing are (K) and (X). The parameters K [hr] travel time of the flood wave through routing reach and dimensionless weight X [—] were found through calibration by sighting their allowable range in HEC-HMS technical reference manual (Table 1).
Baseflow BF [m3s−1] is a flow of water that returns to the stream or land surface from groundwater aquifers. A constant monthly method was adopted in this study. It is a simple approach that used a constant baseflow at all simulation time steps falling within a particular month. For more detail, see the HEC-HMS model sensitivity, calibration, and validation in result and discussion section.
The parameters values which were fixed based on literature review and catchment characteristics deemed as standard or baseline parameter set. Then the model was run repeatedly with the starting baseline value for each parameter multiplied, in turn, by 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, while keeping all other parameters constant at their nominal starting values.
2.9. HEC-HMS Model Calibration and Validation
Calibration is the process of estimating model parameter with the objective to match characteristics of observed and simulated streamflow hydrographs. Validation is needed to test the model performance outside its calibration period. The model was warmed using observed climate data for one year (2000). The model calibration was conducted using the two-third of the observed streamflow data that was nine years of data in range of 2001–2009. The minimum and maximum value of each parameter for calibration was mentioned in Table 1 and the model validation was made out of calibration period using one-third of observed streamflow data, that is, three years of data covers the period of 2010–2012. In the present study, to get initial values of parameters, model sensitivity to its parameters was evaluated first. This is followed by manual calibration which involves manually adjusting the most sensitive parameters until allowable range is achieved between simulated and observed hydrograph. For further details, see the HEC-HMS model sensitivity, calibration, and validation in result and discussion section.
2.10. Hydrological Modeling and Performance
HEC-HMS model is used to simulate the surface runoff response of a catchment [41]. In this study, the Clark transformation method was applied to transfer surface flow to runoff; the initial and constant method was used to estimate the loss in the catchment; monthly base flow separation method was applied to separate base flow; and Muskingum routing method was used to route the downstream unit hydrograph [36, 42–44]. The model was warmed up for the year 2020 followed by calibration (2001–2009) and validation (2010–2012) to assess the performance [35]. Model simulation has been evaluated using efficiency criteria such as Nash Sutcliff (NSE), Coefficient of determination (R2), and Relative Volume Error (RVE) in %. Statistical methods for instance, Bias and Coefficient of Variation (CV), Relative Mean Square Error (RMSE), and correlation coefficient (corr) were used to evaluate the model simulation outputs of rainfall data.where Qo,i is the observed streamflow at the time step i, Qs,i is the simulated flow at the time step i, n is the number of observations and bar symbol denotes the mean.
The percentage error in total runoff volume (RVE), on the other hand, ranges between −∞ to +∞ and the model performance is very good if RVE value is between −5 and 5%, and satisfactory performance if RVE value lies between 5 and 10% and −10 to −5% [45]. The RVE is given by equation (7):where Qo,i is the observed streamflow at the time step i, Qs,i is the simulated flow at the time step i, n is the number of observations, and bar symbol denotes the mean.
The coefficient of determination (R2) is a usually employed statistical index to indicate the strength of the relationship between the observed and model–computed values. A value of zero means no correlation at all; whereas one means the prediction is equal to that of the observation:where Qo,i is the observed streamflow at the time step i, Qs,i is the simulated flow at the time step i, n is the number of observations, and bar symbol denotes the mean (equations (9)–(11)):where Bias = Bias, RRCM = Climate rainfall data over the catchment, = Average rainfall data of the climate, obs = Average observed rainfall datawhere RMSE = Relative Mean Square Error, RRCM = climate rainfall data over the catchment, Robs = Observed rainfall data over the catchment. N = Number of years that rainfall observedwhere CV = Coefficient of Variation. = is average rainfall over the catchment. = indicates standard deviation.
2.11. Peaks Over Threshold (POT) Model Analysis
Peak over threshold (POT) analysis has been established in the field of flood frequency modeling as a viable alternative to the traditional analysis of annual maxima. The POT model can be composed of the Poisson, binomial, and negative binomial distributions for modeling the annual number of events above the threshold. The POT method includes the steps discussed in the following section. Independence criteria, the first step of the POT method is one of the consideration of independence conditions with the criteria that consecutive peaks must be separated by three times TP (average time to peak of five hydrographs), or that the smallest discharge value between two consecutive peaks must be higher than two-thirds of the first peak value [46]. These two conditions were also considered in the POT analyses on the Woybo River.
The independence criteria should be considered only if successive peaks are correlated and none of the other possible steps for reducing correlation is possible. The difference between the average daily discharge value and the local maximum is relatively small. This means that only in the case of very large threshold values is the average daily discharge value rejected and so only the local maximum is considered in the POT sample. If a lower threshold value is chosen, both the average daily discharge value and the local maximum are considered. Both values are part of one flood event, and it is not reasonable to consider one event more than once. This is one of the reasons why the use of independence criteria is necessary (equation (12)).
The probability mass function of the Poisson distribution and the first three moments are
If the mean value of m is larger than the variance of the annual number of exceedances, the binomial distribution can be used. This means that the time distance between the events above the threshold is approximately constant.
Threshold selection defining the threshold value is one of the main disadvantages of the POT method. The selection of the threshold is a subjective process. It is important that the threshold value selected is high enough, so that the model assumptions are not violated [47]. But the truncation level should be selected as low as possible, so that the highest number of exceedances is selected and more reliable parameter estimates can be made [48]. Reference [22] recommended the use of the standard frequency factor k and data properties (mean value and standard deviation). The threshold value can be calculated using equation (13):
The frequency factor k with value can be selected. The low k-value means that a low threshold value is selected and more events are included in the flood frequency analysis. In the Flood Estimation Handbook [49], the threshold value is defined so that, on average, one, three, or five events per year are selected. On average, four events per year were selected for the Woybo River analyses. A return period of 1.2–2 years was proposed for three tests for threshold selection [47]. The results of the tests give an interval of possible threshold values. One of these tests confirms the hypothesis of the Poisson process. This graphical test is based on the dispersion index [46].
2.12. Flood Frequency Analysis
Flood frequency analysis is used to relate the magnitude of floods to their frequency of occurrence using probability distribution methods. At present, there is no universally accepted frequency distribution model for frequency analysis of extreme floods, rather a whole group of models is considered [50].
If a prediction is to be based on a set of hydrologic data, the distribution that best fits the set of data may be expected to give the best estimates usually an extrapolation of the probability of an event occurring. Different probability distribution methods were assessed to predict better performance [9, 45]. In this study, Normal, Log normal, Extreme value type 1(EV-I), and Log Pearson Type III distributions were used. The selected probability distribution or the best fit is Gumbel, in which maximum peak discharge was found and the distribution competes the goodness of fit test. This method abides by the lower Chi-Square value and lower RMSE value for Woybo River [51]. It was applied for the flood frequency under climate change conditions to analyze the frequency of probable maximum runoff for return periods of 2, 5, 10, 25, 50, 100, 500, and 1000 years of streamflow.
2.13. Parameter Estimation
A probability distribution is a function representing the probability of occurrence of a random variable. By fitting distribution to a set of hydrologic data a compact and summarized in formation can be obtained. The moments of the probability density function about the origin are equal to the corresponding moments of the sample data, then method of moments (Mom) results in good estimate of the parameters. Its main drawbacks are that different engineers arrive at different values.
The methods of L-moments are often used and are recommended for estimating distribution parameters. L-moments are analogous to conventional moments defined as linear combinations of the probability weighted moments (PWMs) and provide a greater degree of accuracy and ease. The PWM method is regarded as one of the best methods for parameter estimation [52] and has gained greater recognition in flood frequency analysis than other methods [53]. L-moments are more convenient than PWMs because they are directly interpreted as measure of scale and shape of probability distributions and analogous to conventional moments. In addition, they are based on linear combinations of data that have been arranged in ascending order. They provide an advantage, as they are easy to work with, and more reliable as they are less sensitive to outliers. Theoretical formula in terms of the basic population quantities can be obtained. The special cases of probability-weighted moments of the rth order, βr, exist for a distribution function represented in an integral form.
Method of maximum likelihood is theoretically the most efficient method of fitting probability distributions to data sets with least average error. But there is no analytical solution for some probability distributions.
2.14. L-Moments (LM)
L-moments are introduced [54], which are linear functions of probability weighted moments (PWM’s). L-moments are alternative to the conventional moments, but computed from linear combinations of order statistics. L-moments can be defined for any random variable Y whose mean exists. The rth-order PWM () is defined as per equation (14):where F(y) is a cumulative probability distribution and y(F) is a quantile function of distribution. The first four L-moments in terms of linear combination of PWM are presented in equation (15):
The first L-moment () is a measure of location (mean), while the second L-moment represents the dispersion. Finally, the L-moment ratios are given below.
L-coefficient of variation , L- Skewness , L- Kurtosis . The unbiased sample estimators of of the first four PWMs for any distribution can be computed.where the data (y1:n) are an ordered sample in ascending order from 1 to n. The parameters with L-moments estimation method are obtained by equating the sample L-moments with distribution L-moments.
2.15. Fitting Probability Distributions
By fitting a distribution to a set of hydrologic data, a great deal of the probabilistic information in the sample can be summarized in the function and its associated parameters. The selected distributions should be checked by using the easy fit software application whether the distribution will pass goodness of fit test. Distributions fit by using these methods were tested by using the Anderson Darling, Chi Square, and Kolmogorov–Smirnov tests. The software calculates the statistics and gives ranking distribution of the three goodness of fit tests [55]. In addition, with respect to the graphical representation, which distribution best fits the discharge data and gives the best output in terms of probability and quantiles is a matter of concern.
The goodness of fit tests presented at easy fit software calculated as following manner:(A)Kolmogorov–Smirnov Test: It is used to decide if a sample comes from a hypothesized continuous distribution. The Kolmogorov–Smirnov statistic (D) is based on the largest vertical difference between the theoretical and the empirical cumulative distribution function: where is cumulative distribution function and n is the sample size. The value, in contrast to fixed values, is calculated based on the test statistic and denotes the threshold value of the significance level in the sense that the null hypothesis (H0) will be accepted for all values of less than the value.(B)Anderson–Darling Test: It is general test to compare the fit of an observed cumulative distribution function to an expected cumulative distribution function: where is cumulative distribution function and n is the sample size. The hypothesis regarding the distributional form is rejected at the chosen significance level alpha if the test statistic, A2, is greater than the critical value obtained from the table. The fixed values of alpha are generally used to evaluate the null hypothesis (H0) at various significance levels.(C)Chi-Squared Test: The test is used to determine if a sample comes from a population with a specific distribution: where Oi is observed frequency and Ei is expected frequency. The value, in contrast to fixed values, is calculated based on the test statistic and denotes the threshold value of the significance level in the sense that the null hypothesis (H0) will be accepted for all values of less than the value.
General methodological conceptual framework illustrates the overall work flow (Figure 4).
3. Results and Discussion
3.1. RCM Model Performance Evaluation
The observed catchment-averaged areal annual rainfall amount was 1377.7 mm/year.
Table 2 indicated that, all models underestimate the observed rainfall. The accuracy of models was not the same in representing the rainfall of the catchment. In terms of bias, ensemble mean performs better (Bias = −4.01%), whereas REMO2009 accomplishes worst (Bias = −17.3%). This large bias (Bias = −17.3%) indicates that the RCM rainfall amount largely deviates from the observed rainfall. In terms of CV, ensemble mean performs best (CV = 2.3%), whereas REMO2009 performs worst (CV = 8.3%). REMO2009 performs worst (RMSE = 24.36 mm/year), while ensemble mean achieves better (RMSE = 1.09 mm/year). Furthermore, the ensemble mean performs better (R2 = 0.89) which implies that it shows linear relationship between observed and simulated rainfall. RACMO22T performs worst in terms of correlation coefficient (R2 = 0.25). The ensemble mean estimated the observed mean annual rainfall amount by 85.73% rainfall variability as compared to those five models. In order to reduce the differences between the simulated and observed rainfall, the biases are removed before the use of RCMs models’ simulations.
The monthly rainfall varies up to 101.3 mm between February and November. The catchment receives 1.7 to 55 mm per month in the rest of the months with the scanty rainfall in January and December. The climate models systematically underestimate the monthly rainfall amounts. The result indicates that bias correction is required for further use of the models’ data (Figure 5).
The climate model simulations reasonably reproduced the observed annual rainfall (Figure 6). Both the magnitude and pattern of the observed rainfall annual cycle are reasonably captured. Hereafter, the rainfall data used to evaluate climate change impacts in the catchment after bias correction was made.
Ensemble mean was selected based on performance evaluation criteria including its ability to capture the annual observed rainfall amount relative to five climate models for the study.
According to Mann–Kendall trend test, the annual precipitation slightly decreased. The annual streamflow insignificantly increased with annual rate of 0.048 m3/s during the period 1976 to 2005. The result of annual rainfall is consistent with other annual analysis of rainfall [56], although a small increase in annual precipitation is expected over the country. The average maximum and minimum temperature of the catchment were increased by 0.3750 C and 0.3840 C per year (Table 3). Almost similar warming trends of mean annual minimum temperatures were reported by different periods and spatial scales [57].
Mann–Kendal (MK) trend test was analysed for historical hydro climatic variables including precipitation, temperature, and evapotranspiration (ET) at 5% confidence level. According to Mann–Kendall trend test, the annual areal rainfall and streamflow of Woybo catchment slightly increased. The average minimum and maximum temperature of the catchment is 13.960 C and 25.110 C respectively. Both maximum and minimum temperature revealed significant increasing trend. Similar warming trends of temperature were reported that covered different time frames [57].
3.2. HEC-HMS Model Sensitivity, Calibration, and Validation
In terms of relative volume error (RVE) in %, the model was most sensitive to change in parameters that have steep slope and nonsensitive for parameters that have constant slope (Figure 7). Simulated streamflow volume of the river was the most sensitive to the constant rate (CR) and moderately sensitive to base flow (BF) parameter. However, others such as storage coefficient (SC), time of concentration (Tc), dimensionless constant (X), travel time of flood wave (k), and initial loss (IL) were not sensitive.
There was a good agreement between the simulated and observed flow hydrographs (Figure 8). The peaks in the year 2001, 2003, 2004, and 2009 unsatisfactorily captured the observed hydrograph which may be related to the poor spatial coverage of the precipitation data within the catchment.
Noble enactment was obtained in terms of reproducing the observed pattern of the streamflow hydrograph during calibration and validation (NSE = 0.69 and 0.66), respectively. The model was accepted when evaluated using objective functions. The REV for the calibration period was 4.50% which suggested that the model showed very good performance in estimating observed streamflow volume. Very good performance in estimating observed streamflow volume during validation period (−4.94%) was established.
3.3. Change of Simulated Streamflow
The projected precipitation, temperature, and ET were used for future climate change analysis using the ensemble mean of five RCMs climate models data under RCP4.5 and RCP8.5 scenarios.
HEC-HMS model was used to simulate the future streamflow for the short-term (2011–2040) or 2020s, mid-term (2041–2070), or 2050s and long-term (2071–2100) or 2080s. Baseline period of 1976–2005 streamflow data of the watershed was compared with simulated streamflow data under RCP4.5 and RCP8.5 scenarios for 2020s, 2050s, and 2080s. The analysis was conducted to identify the mean change of monthly, seasonal, and annual streamflow.
3.4. Climate Change Impact on Monthly Streamflow for 2020s, 2050s, and 2080s
The mean monthly streamflow may increase up to 9.08% under RCP4.5 for the months January to March and August to November. For the rest of months, the flow may decrease up to 28.60%. Under RCP8.5, it may increase in the range of 0.25 to 10.98% throughout the year except June, July, September, and December, where there might be a decrease in magnitude of 2.39, 3.01, 0.81, and 6.79%, respectively, over 2020s. It has been demarcated an increase of 11.19% for all months except September and November which decreases in magnitude by 1.89 and 0.02%, respectively, under RCP4.5, while under RCP8.5, it is likely to increase in the range of 2.01–18.72% all the way through except April and May which will decrease in magnitude of 9.68 and 6.79%, respectively, over 2050s. It will decrease in months of January, May, September, and December up to 15.53% under RCP4.5 and under RCP8.5, it will increase maximum to 21.90% for months of January, February, April, May, June, August, and October. But it will decrease in months of March, July, September, November, and December in range of 1.50–5.45% over 2080s compared with the baseline period 1976–2005 (Table 4).
The mean monthly streamflow under RCP4.5 will likely increase up to 9.08% during January to March and August to November. Under RCP8.5, it will increase up to 10.98% for all the months except June, July, September, and December which will decrease by 2.39, 3.01, 0.81, and 6.79%, respectively, in 2020s; 11.19% under RCP4.5, while up to 18.72% under RCP8.5 for all months in 2050s, whereas 13.66% under RCP4.5 and 21.90% under RCP8.5 for all the months in 2080s.
3.5. Climate Change Impact on Annual and Seasonal Flow 2020s, 2050s, and 2080s
There are three seasons, namely winter (dry season from October to January), autumn (small rainy season from February to May), and summer (rainy or big rainy season from June to September). Only autumn (small rain season) and summer (rainy season) were considered except winter (dry season). The climate models simulations exhibited a varied signal seasonal streamflow change between baseline periods.
Under RCP4.5 scenario, the projected streamflow will likely to decrease in autumn and annually by magnitude of 4.14 and 2.15%, respectively. It will likely increase in summer season by 6.46%, but under RCP 8.5, the flow will decrease in autumn and annually by 20.15 and 2.68%, respectively. It may increase in summer season by 12.67 over 2020s. Flow will likely increase in autumn, summer, and annually by magnitude of 8.34, 13.54, and 5.02%, respectively, under RCP4.5 scenario, while under RCP 8.5, it will increase in summer by 15.66% and annually by 5.82% and decrease in autumn season by 12.08% over 2050s. Moreover, the flow will likely increase in autumn, summer, and annually by magnitude of 12.20, 18.06, and 11.87%, respectively, under RCP4.5 scenario, while under RCP 8.5, the projected flow will increase in summer by 29.51% and annually by 16.03%, it will decrease in autumn by 10.55% over 2080s relative to 1976–2005 (Table 5).
The output is consistent with [58] which were found under RCP4.5 scenario indicating an increasing change for both the autumn and summer seasons in all periods. Woybo catchment is vulnerable to climatic change in terms of temperature, rainfall changes, and potential ET. The decrease in future streamflow in the autumn season in the watershed follows rainfall patterns in the area. The future simulated streamflow for small rain and rainy seasons show positive increment under both RCP’s scenarios and will decrease annually under RCP8.5 predicting more sensitive for climate change. This change may depend on the characteristics of the precipitation, temperature, and ET of the catchment. The increment seen during summer and autumn seasons may cause frequent river flooding in the catchment. Streamflow will decrease in autumn season under RCP8.5 scenario in 2080s [36, 59].
3.6. Flood Frequency Analysis Result
3.6.1. Best-Fit Distribution Selection Result
In this study, the best fit distributions were checked by using the Easy Fit software whether the distribution has pass goodness of fit test or not (Table 6).
As illustrated in Table 6, comparatively good statistical results were found in three goodness of fit test for Extreme value type 1. So the selected probability distribution or the best fit is Extreme Value Type I (EVI) or Gumbel, in which maximum peak discharge was also found (Figure 9). This finding is in agreement with [51], which reported that Gumbel’s method is the best fit that is; this method is with the lower Chi-Square value and lower RMSE value for Woybo River.
Three goodness of fit tests were applied in Easy fit to check fitness of Extreme value type 1, Log Pearson Type III, Log normal, and Normal distributions for POT time series. In addition, which distribution best fits the POT data and gives the best output in terms of probability and quantiles graphically was checked (Table 7).
In Kolmogorov–Smirnov Test, the value in contrast to fixed alpha values is calculated based on the test statistic and denotes the threshold value of the significance level in the sense that the null hypothesis (H0) will be accepted for all values of alpha less than the value. The null hypothesis will reject if the value is less than the chosen significance level alpha values for each. The result shows, H0 is accepted for all significance level alpha values for both distributions.
Anderson–Darling test hypothesis regarding the distributional form is rejected at the chosen significance level alpha if the test statistic, AD or A2, is greater than the critical value obtained from a table. The fixed values of alpha are generally used to evaluate the null hypothesis (H0) at various significance levels. The result shows, H0 is accepted for all significance level alpha values and one cannot reject the null hypothesis (H0).
Chi-squared test in which the test hypothesis is rejected for the test statistics greater than value at significance level alpha = 0.05. The result shows all computed values are greater than alpha values and one cannot reject null hypothesis (H0) (Table 6).
The selected probability distribution or the best fit is Gumbel, in which maximum peak discharge was found and the distribution competes the goodness of fit test. This method abides by the lower chi-square value and lower RMSE value for Woybo River [51]. The return period from 2 years to 1000 years with baseline period from 1976 to 2005 has been considered for short-term, mid-term, and long-term starting from 2020 to 2080 (Table 8).
3.6.2. Magnitude Change of Recurrent Flood Peaks
The change of flood magnitude was illustrated for different return periods for 2020s, 2050s, and 2080s relative to (1976–2005) under RCP4.5 and RCP8.5 scenarios (Table 9). The change of peak flood for 2, 5, 10 and 25 years return period in 2020s under RCP4.5 will decrease by 8.99, 16.74, 13.12, and 3.31%, respectively. But it will show positive trend for 50, 100, 500, and 1000 years return periods up to 14.13%. In 2020s under RCP8.5 for 2, 5, and 10 years return period, the discharge may decrease by a magnitude up to 8.18% and which shows positive trend for 25, 50, 100, 200, 500, and 1000 years return periods in range of 4.58–20.28%. In 2050s under RCP4.5 and RCP8.5, the discharge will decrease for 2 and 5 years return period up to 30.41%. It shows positive trend for 10, 25, 50, 100, 200, 500, and 1000 years return periods in range of 6.84 to 34.98% and up to 36.51% under RCP4.5 and RCP8.5, respectively. In 2080s, the change of peak discharge will increase up to 30.65% except for return period of 2 and 5 under RCP4.5. The change of peak discharge for 2, 5, 10, 25, 50, 100, 200, 500, and 1000 years return period will likely increase up to 46.80% in 2080s under RCP8.5 with relative to 1976–2005.
The change of magnitude of flood will increase for the catchment but significant decrement will happen for 2 and 5 years return period under RCP4.5 and RCP8.5 in 2020s and 2050s, though, in 2080s only RCP8.5 shows positive trend for all return periods. The change will likely show increasing trend for 10, 25, 50, 100, 200, 500, and 1000 years recurrent periods under both RCP4.5 and RCP8.5 scenarios in 2050s and 2080s periods, respectively. As a result, increment of flood magnitude may lead the community for different environmental and economic problems. Woybo watershed may experience impact of climate change on magnitude of floods in future climate over 2050s and 2080s. Heavy floods have long return times. As a whole, a rise in flood severity in the study area could have a major negative impact on the sustainability of existing agriculture practices. In addition it would result in unanticipated floods and flood hazards for the communities. So flood prevention and preparedness steps in the floodplain of the river basin and downstream should be taken as a precaution to mitigate the damage if caused.
4. Conclusions
This study assessed the impact of climate change on flood frequency at Woybo watershed for 2020s, 2050s, and 2080s relative to 1976–2005 using ensemble mean of five RCMs output under RCP4.5 and RCP8.5 scenarios. Mann–Kendall (MK) trend test was analyzed for historical hydro climatic variables including precipitation, temperatures, and ET at 5% confidence level. The maximum and minimum temperature showed statistically significant increasing trend. The change of magnitude of peak flood will increase for the catchment. But significant decrement will occur for 2 and 5 years return period under RCP4.5 and RCP8.5 in 2020s and 2050s. In 2080s, only RCP8.5 will show positive trend for all return periods. The flood magnitude increases for 10, 25, 50, 100, 200, 500, and 1000 years recurrent periods under both RCP4.5 and RCP8.5 in 2050s and 2080s, respectively. Woybo watershed may experience impact of climate change on magnitude of floods during 2050s and 2080s. The increase in flood magnitude in the catchment has a significant negative impact. Flood frequency analysis based on a peak over threshold approach including correct estimation of parameter with good probability distribution is the best way to evaluate flood frequency under changing climate. The output of this study will have important implications for the design of hydraulic structures, floodplain development, and water resource management in the catchment. The result of rainfall-runoff modeling was incorporated, and RCMs output was evaluated. However, a thorough flood frequency analysis requires a multidisciplinary approach, which incorporates the results of both physically based (rainfall-runoff modeling) with detailed instrumental gauging data, supplemented with regional data, and historical and paleo flood information. The application of the combination of this full-range information has their limitations. In addition, there is strong recommendation that the quality as well as quantity of weather stations be improved in enhancing the model's effectiveness by providing ample number of highly effective hydro-meteorological stations.
Data Availability
Data used in this study have been collected from various sources.
Conflicts of Interest
There are no conflicts of interest among authors.
Acknowledgments
The authors would like to acknowledge all data providers namely MoWIEE (Minstry of Water Irrigation and Energy of Ethiopia), NMAE (National Meteorology Agency of Ethiopia) for providing required data. The Authors are thankful to Arba Minch University who has provided all logistic support in conducting the research work. No fund is received from any source.