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Research
Analyzing the impacts of urbanization on runoff characteristics in Adama city, Ethiopia
Dejene Tesema Bulti
Ethiopian Institute of Architecture,Building Construction and City Development,Addis Ababa University,
Corresponding Author
ORCiD: https://orcid.org/0000-0001-7525-6682
License:
This work is licensed under a CC BY 4.0 License. Read Full License
Background It has been increasingly recognized that urbanization is responsible for alterations of land use/land cover globally with substantial environmental impacts on all temporal and spatial scales. Particularly, it significantly affects the hydrologic cycle. Floods are the major threats to several cities worldwide with more effects in developing countries. Likewise, urban water management has become the main focus of sustainable urban development and poses higher demand for information related to the interaction between the urbanization process and hydrological attributes, but little is known in the context of Ethiopian urban centers. For this, Adama city, a fast grown and flood vulnerable urban area is considered to examine the impacts of urbanization on the storm runoff at different spatial scales from 1995 to 2019. Preparing land use/land cover (LULC) maps for different periods, the dynamics of LULC transformations were analyzed. The SCS-CN method was used to compute runoff at respective years from which spatiotemporal changes of the city’s hydrology were assessed at the city and watershed levels. Regression analysis was used for exploring the relation between the spatiotemporal changes of imperviousness ratio and runoff.
Results The findings show that the urban built-up area undergone about 22% expansion annually from 1995 to 2019. Besides the runoff is increased by 23% in the City and 31% and 16.6% in the watersheds. Moreover, the significant direct linear relationship is found between the spatiotemporal variations of runoff and imperviousness ratio at both spatial scales.
Conclusions Adama city has experienced significant LULC transformations over the last 24 years with significant effects on hydrological attributes, which pressed an alarm for increasing flood hazards. Hence, in order to realize sustainable growth of the city, future developments should be guided by impervious surface-based land use regulations.
Keywords
Urbanization, Urban flood, Land-use changes, Land cover dynamics, Runoff
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
2.1 The study area
Adama City is one of the fast-growing and flood vulnerable urban areas in the country (Bulti et al. 2017). It stretches between 8°26′15″N to 8°37′00″N latitude and 39°12′15″E to 39°19′45″E longitude. The population of the city has grown at the rate of 9% from 2004 to 2016 (Bulti & Asefa 2019). The latest approved land use plan of the city is prepared in 2004 (Bulti & Sori 2017). The administrative boundary set by this plan is selected to limit the spatial extent of the analysis. The City falls in two main watersheds: Awash and Mermersa (Fig. 1), with spatial coverage of 7, 329.7 ha and 6, 036.8 ha, respectively.
2.2 Data used and image pre-processing
Data used in this study were collected from different sources, including websites, organizations and stakeholders. Landsat 7 TM/ ETM+ (Enhanced Thematic Mapper Plus) (L1TP product of path 168, row 54) was used for mapping LULC of the study area. LandSAT image is widely used for urban LULC mapping, despite its medium spatial resolution and mixed pixel problem (Lu & Weng 2005; Chen et al. 2016). It is freely accessible for multiple dates. One image from each year with cloud contamination less than 10% were accessed from the United State Geological Survey (USGS) (https://espa.cr.usgs.gov/). All images are within the dry season, as the accuracy of LandSAT image classification during the dry season is found to be higher than during the wet season (Liu et al. 2015).
Geometric accuracy of land use maps is important in urban studies (Sertel & Akay 2015). Landsat Level 1 (L1T) images are geometrically corrected and orthorectified by the National Aeronautics and Space Administration (NASA) (Gutman et al. 2013). The atmospheric effects were reduced through conversion of raw digital number (DN) values to the surface reflectance, which was undertaken in radiometric calibration module in ENVI software.
2.3 Land use/land cover mapping
Considering the importance of short-term changes in urban areas due to rapid urbanization and climate changes (Zhang et al. 2018), LULC maps of the study area were prepared at about 5 years’ interval (1995, 2000, 2005, 2010, 2015 and 2019) using LandSAT images through supervised classification method. It involves defining classification scheme, selecting training samples, running an algorithm to assign each pixel into a class and accuracy assessment.
Defining classification scheme
The analysis focused on spectral resolution because the spectral dimension is the most important source of cover type information in coarse resolution images. The success of LULC usually measured by the ability to match the spectral classes in the data to the information classes of interest (Weng 2010). Information classes are those categories of interest that the analyst is actually trying to identify in the imagery, whereas spectral classes are groups of pixels that are uniform (or near-similar) with respect to their brightness values in the different spectral channels of the data.
In a complex urban landscape, a particular land use class may have diverse spectral characteristics (e.g., roof cover of old and new buildings). By contrast, different classes (objects) can have the same spectral characteristics (e.g., rock and concrete or bright building roofs). Hence, it is rare that there is a simple one-to-one match between these two types of classes. Many times it is found that 2 to 3 spectral classes merge to form one informational class.
Given the importance of the appropriate classification scheme, in this study, initially, by visually analyzing the color composite LandSAT images with different band combinations, different classes were identified, and aggregated into four: urban, bare land, agriculture and vegetation (Table 1).
| LULC class | Description | |
|---|---|---|
| Urban | Comprises areas with all types of artificial surfaces, including buildings and transportation infrastructure (asphalt, gravel, railway). Areas under construction are also included | |
| Barren land | Includes a surface with no or little vegetation, open land, exposed soil, rocks and sand (eroded gullies) | |
| Agricultural | Includes areas used for cultivation (both annuals and perennials) and grazing | |
| Vegetation | Comprises areas with vegetation cover, such as areas covered with both indigenous and exotic tree and shrub land. It also includes green spaces in built‑up areas: an area of grass, trees, or other vegetation set apart for recreational or aesthetic purposes inside urban built environment |
Training sample section
Training samples for each class were collected from each image. In order to reduce the sampling biases, consistency in sample selection was kept by selecting pixels that remained unchanged at different times to train the classifier. First, samples were selected from LandSAT image of 1995 (first image). Subsequently, these samples were treated as training samples for the first image and used as a base for the adjacent image (2000). Second, the base samples were overlaid with the second image to check if change in class occurred. If changes were observed, new sample with more confidence was substituted from the surrounding area. Similarly, the same procedures were followed by selection of training samples for the rest of the images.
Classification algorithm
Each image was classified into a set of spectral classes using Support Vector Machine (SVM) algorithm in ENVI software. SVM is non-parametric classifier. Unlike parametric classifiers such as maximum likelihood which assumes that the data is normally distributed, non-parametric classifiers do not base classification on a normality assumption or statistical parameters (Phiri & Morgenroth 2017). Because of highly heterogeneous land covers data (e.g., urban areas) are unlikely normally distributed, the distribution of land cover surfaces is associated with various uncertainties which prevents their description based on data distribution (Lu & Weng 2007). In this respect, non-parametric classifiers provide better results as compared to parametric classifiers in complex landscapes.
Accuracy assessment
LULC classification accuracy was assessed quantitatively using error matrix which is the commonly used method in LULC classification accuracy assessment (Weng 2010). In this regard, sample pixels were selected from each of classified images through a stratified random sampling scheme in ENVI software. The samples were overlaid with the existing map (for 1995), google earth (for 2000, 2005 and 2010) and digital orthophoto (for 2015 and 2019) to visually interpret and determine their respective classes. Based on the error matrix generated for each classified map, overall accuracy, user’s accuracy and producer’s accuracy were calculated, in addition to kappa variance. The accuracy requirements for change detection analysis were determined based on the suggestion of Congalton and Green (2009). In this case, the value of the Kappa statistics, greater than 0.8, indicates strong agreement between classified classes and ground truth.
2.4 Methods
Analysis of LULC dynamics
The spatiotemporal changes of LULC were identified using areal data generated from classified maps in GIS environment. Quantitative areal data from the overall LULC changes, as well as gains and losses in each class were compiled to analyze the nature and rate of the changes. The percentages of changes were computed using Eq. 1 similar to other studies (Butt et al. 2015; Gashu and Gebre‑Egziabher 2018). In this case, the positive and negative values suggest a gain and loss in spatial extent, respectively.
[Due to technical limitations, the formula could not be displayed here. Please see the supplementary files to access the formula.]
Analysis of imperviousness change
Impervious surfaces are generally anthropogenic features (buildings, parking lots, roads, etc.) which rainfall water cannot permeate (Tabbutt & Ambrogi 2013; Zhang et al. 2018). They are usually related to urban growth and expansion can be delineated using different methods. Extracting urban impervious surfaces from LandSAT imagery using standard classification techniques can provide adequate results (Parece & Campbell 2013). Percent impervious area (PIA) refers to the areal proportion of impervious surfaces within the defined boundary (e.g., watershed, administrative boundary). Likewise, in this study, it was computed by using the ratio of areal data of urban class at different years to the extent of the respective analysis boundaries. The changes of imperviousness were computed with respect to the first year (Eq. 2). This helped to assess the impact of urbanization in increasing the impervious surface in the study area.
[See supplementary files for formula.]
Evaluation of spatiotemporal changes of runoff
Evaluation of the temporal variations of the runoff due to the impacts of LULC changes involves computation of runoff and percentage change with respect to a baseline/reference year.
Rainfall-runoff was calculated using soil conservation service curve number (SCS-CN) technique. It is largely accepted method to examine the relationship between different land uses and runoff, and widely used for water resources management and planning (Abas & Hashim 2014; Bhaskar & Suribabu 2014; Ongsomwang & Pimjai 2015; Viji et al. 2015; Tailor & Shrimali 2016; Hameed 2017; Prakash & Sreedevi, 2017; Rao et al. 2017; Satheeshkumar et al. 2017; Zhang et al. 2018). SCS-CN method provides an adequate result with a minimum information (Bhuyan et al. 2003) that makes it more useful for ungauged watershed (Pandey & Stuti, 2017; Satheeshkumar et al. 2017). The value of CN reflects the impact of land cover on the runoff yield ranging from 0 (100% infiltration) to 100 (0% infiltration). Evapotranspiration losses are considered to be insignificant in the storm event (Chen et al. 2015).
Runoff can be easily obtained using three important properties of the watershed: soil permeability, land use and antecedent soil water conditions (Bansode et al. 2014; Chen et al. 2015). In this regard, soil types in the study area were converted into respective hydrologic similar units. The study area was spatially intersected with LULC and soil maps to calculate the area under the different hydrological similar units (HSU) and to assign CN values. Since the study area comprises different characteristics (soil type and land cover), the weighted curve number was considered and computed using Eq. 3. Moreover, Equations 4 and 5 were applied for converting the average antecedent moisture condition into wet condition and for computing the potential maximum soil retention, respectively. Using hourly average rainfall, the accumulated runoff depth for respective areas was computed using Equations 6.
[See supplementary files.]
Using the computed runoff for respective years, the temporal variations of the runoff due to the impacts of LULC changes were assessed through runoff depth change ratio. Following the method applied by Li & Wang (2009), by taking the runoff depth of the first year (1995) as a baseline, the percentage changes in runoff for 2000, 2005, 2010, 2015 and 2019 were computed using Eq. 7. This helped to determine the temporal variations in storm runoff attributable to the changes in LULC of the study area with respect to the baseline.
[See supplementary files.]
Regression analysis
Regression analysis was carried out to explore the relationship between the spatiotemporal changes of PIA and runoff. It is the common method to investigate the relationship between a quantitative outcome and a quantitative explanatory variable (Seltman 2018).
The validity of the model assumptions was determined by examining the structure of the residuals and the data pattern through graphs. Examination of residual plots is a simple and effective method for validation of standard assumptions in regression analysis (Chattefuee and Hadi 2006). In this context, the normality assumption was validated using a normal probability plot of standardized residuals which is a plot of the ordered standardized residuals against the normal scores. Under normality assumptions, this plot should resemble a (nearly) straight line with an intercept of zero and a slope of one, and they are equal to mean and standard deviation of the standardized residuals, respectively. In addition, scatter plots of the standardized residual against PIA and fitted values were used to validate the linearity assumption. Under the standard assumptions, the standardized residuals are uncorrelated with the explanatory variable and with fitted values. The random scatter of points of these plots explains the validity of linearity assumption.
The strength of the linear relationship between the runoff variations and the PIA was determined using the value of Pearson’s correlation coefficient (r). It is a dimensionless quantity that commonly used to compare the linear relationships between pairs of variables in different units. Accordingly, the non-zero value of the correlation coefficient indicates the variables are correlated. Further, the positive and negative values indicate direct and indirect relationship, respectively. Moreover, similar to Bulti & Assefa (2019) the strength of the correlation was described using the absolute value of correlation coefficient: very weak (|r|< 0.19), weak (|r|< 0.39), moderate (|r|< 0.59), strong (|r|< 0.79), very strong (|r|<1).
Statistical significance test was also conducted to offer an objective measure in the decision about the validity of the generalization, and it was determined using p-value statistics. In this case, the null hypothesis states that there is no significant relationship between the changes in PIA and runoff. In theory, the p-value is a continuous measure of evidence (Gelman 2012), yet in this study, the term “significant” refers to the 95% confidence level (p < 0.05); it is standard in statistical practice in most of the Engineering researches (Bulti & Assefa 2019).
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Research
Analyzing the impacts of urbanization on runoff characteristics in Adama city, Ethiopia
Dejene Tesema Bulti
Ethiopian Institute of Architecture,Building Construction and City Development,Addis Ababa University,
Corresponding Author
ORCiD: https://orcid.org/0000-0001-7525-6682
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
History
CURRENT STATUS: Posted
Version 1
Posted 20 Dec, 2019
No community comments so far
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
License:
This work is licensed under a CC BY 4.0 License. Read Full License
Background It has been increasingly recognized that urbanization is responsible for alterations of land use/land cover globally with substantial environmental impacts on all temporal and spatial scales. Particularly, it significantly affects the hydrologic cycle. Floods are the major threats to several cities worldwide with more effects in developing countries. Likewise, urban water management has become the main focus of sustainable urban development and poses higher demand for information related to the interaction between the urbanization process and hydrological attributes, but little is known in the context of Ethiopian urban centers. For this, Adama city, a fast grown and flood vulnerable urban area is considered to examine the impacts of urbanization on the storm runoff at different spatial scales from 1995 to 2019. Preparing land use/land cover (LULC) maps for different periods, the dynamics of LULC transformations were analyzed. The SCS-CN method was used to compute runoff at respective years from which spatiotemporal changes of the city’s hydrology were assessed at the city and watershed levels. Regression analysis was used for exploring the relation between the spatiotemporal changes of imperviousness ratio and runoff.
Results The findings show that the urban built-up area undergone about 22% expansion annually from 1995 to 2019. Besides the runoff is increased by 23% in the City and 31% and 16.6% in the watersheds. Moreover, the significant direct linear relationship is found between the spatiotemporal variations of runoff and imperviousness ratio at both spatial scales.
Conclusions Adama city has experienced significant LULC transformations over the last 24 years with significant effects on hydrological attributes, which pressed an alarm for increasing flood hazards. Hence, in order to realize sustainable growth of the city, future developments should be guided by impervious surface-based land use regulations.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
2.1 The study area
Adama City is one of the fast-growing and flood vulnerable urban areas in the country (Bulti et al. 2017). It stretches between 8°26′15″N to 8°37′00″N latitude and 39°12′15″E to 39°19′45″E longitude. The population of the city has grown at the rate of 9% from 2004 to 2016 (Bulti & Asefa 2019). The latest approved land use plan of the city is prepared in 2004 (Bulti & Sori 2017). The administrative boundary set by this plan is selected to limit the spatial extent of the analysis. The City falls in two main watersheds: Awash and Mermersa (Fig. 1), with spatial coverage of 7, 329.7 ha and 6, 036.8 ha, respectively.
2.2 Data used and image pre-processing
Data used in this study were collected from different sources, including websites, organizations and stakeholders. Landsat 7 TM/ ETM+ (Enhanced Thematic Mapper Plus) (L1TP product of path 168, row 54) was used for mapping LULC of the study area. LandSAT image is widely used for urban LULC mapping, despite its medium spatial resolution and mixed pixel problem (Lu & Weng 2005; Chen et al. 2016). It is freely accessible for multiple dates. One image from each year with cloud contamination less than 10% were accessed from the United State Geological Survey (USGS) (https://espa.cr.usgs.gov/). All images are within the dry season, as the accuracy of LandSAT image classification during the dry season is found to be higher than during the wet season (Liu et al. 2015).
Geometric accuracy of land use maps is important in urban studies (Sertel & Akay 2015). Landsat Level 1 (L1T) images are geometrically corrected and orthorectified by the National Aeronautics and Space Administration (NASA) (Gutman et al. 2013). The atmospheric effects were reduced through conversion of raw digital number (DN) values to the surface reflectance, which was undertaken in radiometric calibration module in ENVI software.
2.3 Land use/land cover mapping
Considering the importance of short-term changes in urban areas due to rapid urbanization and climate changes (Zhang et al. 2018), LULC maps of the study area were prepared at about 5 years’ interval (1995, 2000, 2005, 2010, 2015 and 2019) using LandSAT images through supervised classification method. It involves defining classification scheme, selecting training samples, running an algorithm to assign each pixel into a class and accuracy assessment.
Defining classification scheme
The analysis focused on spectral resolution because the spectral dimension is the most important source of cover type information in coarse resolution images. The success of LULC usually measured by the ability to match the spectral classes in the data to the information classes of interest (Weng 2010). Information classes are those categories of interest that the analyst is actually trying to identify in the imagery, whereas spectral classes are groups of pixels that are uniform (or near-similar) with respect to their brightness values in the different spectral channels of the data.
In a complex urban landscape, a particular land use class may have diverse spectral characteristics (e.g., roof cover of old and new buildings). By contrast, different classes (objects) can have the same spectral characteristics (e.g., rock and concrete or bright building roofs). Hence, it is rare that there is a simple one-to-one match between these two types of classes. Many times it is found that 2 to 3 spectral classes merge to form one informational class.
Given the importance of the appropriate classification scheme, in this study, initially, by visually analyzing the color composite LandSAT images with different band combinations, different classes were identified, and aggregated into four: urban, bare land, agriculture and vegetation (Table 1).
| LULC class | Description | |
|---|---|---|
| Urban | Comprises areas with all types of artificial surfaces, including buildings and transportation infrastructure (asphalt, gravel, railway). Areas under construction are also included | |
| Barren land | Includes a surface with no or little vegetation, open land, exposed soil, rocks and sand (eroded gullies) | |
| Agricultural | Includes areas used for cultivation (both annuals and perennials) and grazing | |
| Vegetation | Comprises areas with vegetation cover, such as areas covered with both indigenous and exotic tree and shrub land. It also includes green spaces in built‑up areas: an area of grass, trees, or other vegetation set apart for recreational or aesthetic purposes inside urban built environment |
Training sample section
Training samples for each class were collected from each image. In order to reduce the sampling biases, consistency in sample selection was kept by selecting pixels that remained unchanged at different times to train the classifier. First, samples were selected from LandSAT image of 1995 (first image). Subsequently, these samples were treated as training samples for the first image and used as a base for the adjacent image (2000). Second, the base samples were overlaid with the second image to check if change in class occurred. If changes were observed, new sample with more confidence was substituted from the surrounding area. Similarly, the same procedures were followed by selection of training samples for the rest of the images.
Classification algorithm
Each image was classified into a set of spectral classes using Support Vector Machine (SVM) algorithm in ENVI software. SVM is non-parametric classifier. Unlike parametric classifiers such as maximum likelihood which assumes that the data is normally distributed, non-parametric classifiers do not base classification on a normality assumption or statistical parameters (Phiri & Morgenroth 2017). Because of highly heterogeneous land covers data (e.g., urban areas) are unlikely normally distributed, the distribution of land cover surfaces is associated with various uncertainties which prevents their description based on data distribution (Lu & Weng 2007). In this respect, non-parametric classifiers provide better results as compared to parametric classifiers in complex landscapes.
Accuracy assessment
LULC classification accuracy was assessed quantitatively using error matrix which is the commonly used method in LULC classification accuracy assessment (Weng 2010). In this regard, sample pixels were selected from each of classified images through a stratified random sampling scheme in ENVI software. The samples were overlaid with the existing map (for 1995), google earth (for 2000, 2005 and 2010) and digital orthophoto (for 2015 and 2019) to visually interpret and determine their respective classes. Based on the error matrix generated for each classified map, overall accuracy, user’s accuracy and producer’s accuracy were calculated, in addition to kappa variance. The accuracy requirements for change detection analysis were determined based on the suggestion of Congalton and Green (2009). In this case, the value of the Kappa statistics, greater than 0.8, indicates strong agreement between classified classes and ground truth.
2.4 Methods
Analysis of LULC dynamics
The spatiotemporal changes of LULC were identified using areal data generated from classified maps in GIS environment. Quantitative areal data from the overall LULC changes, as well as gains and losses in each class were compiled to analyze the nature and rate of the changes. The percentages of changes were computed using Eq. 1 similar to other studies (Butt et al. 2015; Gashu and Gebre‑Egziabher 2018). In this case, the positive and negative values suggest a gain and loss in spatial extent, respectively.
[Due to technical limitations, the formula could not be displayed here. Please see the supplementary files to access the formula.]
Analysis of imperviousness change
Impervious surfaces are generally anthropogenic features (buildings, parking lots, roads, etc.) which rainfall water cannot permeate (Tabbutt & Ambrogi 2013; Zhang et al. 2018). They are usually related to urban growth and expansion can be delineated using different methods. Extracting urban impervious surfaces from LandSAT imagery using standard classification techniques can provide adequate results (Parece & Campbell 2013). Percent impervious area (PIA) refers to the areal proportion of impervious surfaces within the defined boundary (e.g., watershed, administrative boundary). Likewise, in this study, it was computed by using the ratio of areal data of urban class at different years to the extent of the respective analysis boundaries. The changes of imperviousness were computed with respect to the first year (Eq. 2). This helped to assess the impact of urbanization in increasing the impervious surface in the study area.
[See supplementary files for formula.]
Evaluation of spatiotemporal changes of runoff
Evaluation of the temporal variations of the runoff due to the impacts of LULC changes involves computation of runoff and percentage change with respect to a baseline/reference year.
Rainfall-runoff was calculated using soil conservation service curve number (SCS-CN) technique. It is largely accepted method to examine the relationship between different land uses and runoff, and widely used for water resources management and planning (Abas & Hashim 2014; Bhaskar & Suribabu 2014; Ongsomwang & Pimjai 2015; Viji et al. 2015; Tailor & Shrimali 2016; Hameed 2017; Prakash & Sreedevi, 2017; Rao et al. 2017; Satheeshkumar et al. 2017; Zhang et al. 2018). SCS-CN method provides an adequate result with a minimum information (Bhuyan et al. 2003) that makes it more useful for ungauged watershed (Pandey & Stuti, 2017; Satheeshkumar et al. 2017). The value of CN reflects the impact of land cover on the runoff yield ranging from 0 (100% infiltration) to 100 (0% infiltration). Evapotranspiration losses are considered to be insignificant in the storm event (Chen et al. 2015).
Runoff can be easily obtained using three important properties of the watershed: soil permeability, land use and antecedent soil water conditions (Bansode et al. 2014; Chen et al. 2015). In this regard, soil types in the study area were converted into respective hydrologic similar units. The study area was spatially intersected with LULC and soil maps to calculate the area under the different hydrological similar units (HSU) and to assign CN values. Since the study area comprises different characteristics (soil type and land cover), the weighted curve number was considered and computed using Eq. 3. Moreover, Equations 4 and 5 were applied for converting the average antecedent moisture condition into wet condition and for computing the potential maximum soil retention, respectively. Using hourly average rainfall, the accumulated runoff depth for respective areas was computed using Equations 6.
[See supplementary files.]
Using the computed runoff for respective years, the temporal variations of the runoff due to the impacts of LULC changes were assessed through runoff depth change ratio. Following the method applied by Li & Wang (2009), by taking the runoff depth of the first year (1995) as a baseline, the percentage changes in runoff for 2000, 2005, 2010, 2015 and 2019 were computed using Eq. 7. This helped to determine the temporal variations in storm runoff attributable to the changes in LULC of the study area with respect to the baseline.
[See supplementary files.]
Regression analysis
Regression analysis was carried out to explore the relationship between the spatiotemporal changes of PIA and runoff. It is the common method to investigate the relationship between a quantitative outcome and a quantitative explanatory variable (Seltman 2018).
The validity of the model assumptions was determined by examining the structure of the residuals and the data pattern through graphs. Examination of residual plots is a simple and effective method for validation of standard assumptions in regression analysis (Chattefuee and Hadi 2006). In this context, the normality assumption was validated using a normal probability plot of standardized residuals which is a plot of the ordered standardized residuals against the normal scores. Under normality assumptions, this plot should resemble a (nearly) straight line with an intercept of zero and a slope of one, and they are equal to mean and standard deviation of the standardized residuals, respectively. In addition, scatter plots of the standardized residual against PIA and fitted values were used to validate the linearity assumption. Under the standard assumptions, the standardized residuals are uncorrelated with the explanatory variable and with fitted values. The random scatter of points of these plots explains the validity of linearity assumption.
The strength of the linear relationship between the runoff variations and the PIA was determined using the value of Pearson’s correlation coefficient (r). It is a dimensionless quantity that commonly used to compare the linear relationships between pairs of variables in different units. Accordingly, the non-zero value of the correlation coefficient indicates the variables are correlated. Further, the positive and negative values indicate direct and indirect relationship, respectively. Moreover, similar to Bulti & Assefa (2019) the strength of the correlation was described using the absolute value of correlation coefficient: very weak (|r|< 0.19), weak (|r|< 0.39), moderate (|r|< 0.59), strong (|r|< 0.79), very strong (|r|<1).
Statistical significance test was also conducted to offer an objective measure in the decision about the validity of the generalization, and it was determined using p-value statistics. In this case, the null hypothesis states that there is no significant relationship between the changes in PIA and runoff. In theory, the p-value is a continuous measure of evidence (Gelman 2012), yet in this study, the term “significant” refers to the 95% confidence level (p < 0.05); it is standard in statistical practice in most of the Engineering researches (Bulti & Assefa 2019).