Abstract

The full integration between the computation of climate change effects and the prediction of extreme rainfall frequency is not yet well developed. In this study, the maximum daily rainfall of 26 stations in the western Kingdom of Saudi Arabia (KSA) are extracted covering an area of 180,000 km2 for processing and analyzing. Discordancy test (Di) showed that some stations are discordant, and the selected study area needs to be subdivided in order to reduce the inherent discordance. The rainfall stations are subdivided into three sub-regions based on a new approach by using L-Skewness parameter value (low, moderate, and high). Five probability distribution functions (PDFs) are evaluated using goodness of fit (Zdist) test and L-moment ratios diagram (LMRD). It was found that for sub-regions A, B, and C, the best fits are GPA, PE3, and GEV PDFs, respectively. Regional growth curves for each sub-region are developed and the predicted extreme rainfall for 100 years' return periods are computed for each station. Finally, climate change impact is evaluated using the emission scenario A2 which is about +40% and the predicted extreme rainfall frequency is computed taking into consideration the climate change impacts.

INTRODUCTION

Estimation of extreme hydrological events (i.e., rainfall, floods, etc.) is needed by many water-related projects and the most commonly used approach is the extreme value theory (Reiss & Thomas 2007), where the probability distribution functions (PDFs) are implemented using historical data. Several PDFs are available for fitting the observed data, where the relationship between the magnitude and the frequency of the hydrological events is explored (Ahsanullah 2016).

Unfortunately, the extreme rainfall prediction using PDFs do not take into account the future climate change impacts. According to the Intergovernmental Panel on Climate Change (IPCC) reports, frequency and depth of rainfall events will increase over most areas around the world (IPCC 2007, 2014). The IPCC have developed 40 emission scenarios by considering various projections of the world development in the 21st century based on major driving forces including population, economy, energy, land use, and agriculture (Stocker et al. 2014). The global climate (circulation) models (GCMs) depend on observed meteorological data to simulate the future atmospheric circulation patterns.

In many situations, the selected study area lacks records (ungauged) or insufficient observations for reliable estimation of quantiles. In such cases, the regional frequency analysis (RFA) approach is widely employed for incorporating observations from several locations in a homogeneous region, where all the records are assumed to follow the same PDF (Hosking & Wallis 1997; Bradley 1998; Rutkowska et al. 2018). The RFA is not used only for estimation of frequencies at ungauged sites, but also to improve the accuracy of PDFs' parameter estimations (Bracken et al. 2018). The same approach assumes that the sites in the region should follow the same PDF (Dalrymple 1960). When the region has several sites, the identification of homogeneous regions (sub-regionalization) is usually the most critical part of the analysis and needs more subjective judgment (Lin & Chen 2006).

In the literature, several approaches are proposed to delineate the homogeneous regions, such as cluster analysis (Burn 1989), pooling techniques (Das & Cunnane 2010), and region of influence (Burn 1990). The homogeneity (H) test by Hosking & Wallis (1993) is commonly considered to relate the variability of the at-site L-variation coefficient (L-Cv) over a region. In this study, a new approach as L-skewness coefficient (L-Cs) is implemented to sub-divide the region into non-discordant sub-regions. This study aims to integrate the predicted regionalized extreme rainfall with the simulated climate change impact by means of the emission scenario A2.

MATERIAL AND METHODS

Study area and data set

The selected study area is located in the western Kingdom of Saudi Araba (KSA) bounded by latitudes 22° and 27° N and longitudes 37° and 41° E, with an area of 180,000 km2. Topographically, the region can be divided into three sub-regions, which are the mountains, the hills, and the Red Sea coastal plain, where the elevation ranges from 0 up to 2,300 m above the mean sea level (a.m.s.l.). The area is predominantly arid with hot summer and cooler winter seasons. Figure 1 shows the general location of the study area where the rainfall is sporadic and characterized by moderate to high variations in space and time (Subyani & Al-Ahmadi 2011). The rainy season from October to April produces 40 mm mean annual rainfall in the coastal plain to around 100 mm in the mountainous areas (Şen 1983). A combination of disturbances causes extreme rainfall events from the winter Mediterranean and the Sudan trough, which usually generates extreme convective rainfall events over the study area (Alahmadi et al. 2014).

Figure 1

The general location of the study area.

Figure 1

The general location of the study area.

In the study area, there are 26 daily raingauges with records starting from 1966 onwards with historical records ranging from 28 up to 50 years with an average of 41 years and 1,075 station-years. The maximum annual daily amounts are extracted from each station for processing.

Methods

L-moments' approach is used starting with computation of L-moment ratios and discordancy measure (Di) to identify discordant sites within the group as a whole. If any site is discordant then the sites should be sub-divided into more than one region. In this study, a new approach is implemented for sites' categorizations into low L-Cs (less than 0.2), medium L-Cs (between 0.2 and 0.3), and high L-Cs (greater than 0.3) based on the L-skewness (L-Cs) values. The homogeneity tests (H), goodness of fit test (Zdist), and L-moment ratio diagram (LMRD) are then implemented to select the best PDF fit for each sub-region. Then, the regional growth curve is developed using the candidate PDF and the extreme rainfall quantiles are computed for 100 years' return period. Finally, the climate change impact prediction is developed for rainfall in the western KSA by Saudi Presidency of Meteorology and Environment protection (PME) using A2 emission scenario.

RESULTS AND DISCUSSION

L-moments and discordancy measure computations

L-moment statistics and discordancy measure (Di) are computed for each site through the use of lmomRFA R package Version 3.1 developed by Hosking (2017). Table 1 shows L-moment ratios (mean, L-Cv, L-Cs, and L-Ck) and Di. The mean ranges from 13.42 mm in the northern part to 31.12 mm in the southern part, whereas the L-Cv variation domain is from 0.29 in the eastern part to 0.46 in the western and north-western part, which implies high to very high variability. On the other hand, the L-Cs has values in the range from 0.118 in the south and south-east to 0.376 in the eastern north, which implies high to very high skewness, whereas L-Ck ranges from 0.033 in the south-west to 0.338 in the south-east. Figure 2 shows the spatial distribution of the four L-moment ratios. Finally, Di measure for each station is less than 2.0 except at station No. 20 with Di = 3.06, which is an indication that the sites do not belong to only one region and should be sub-divided further into more than one region.

Table 1

Computed L-moment ratios and discordancy measure

ID Mean L-Cv L-Cs L-Ck Di ID Mean L-Cv L-Cs L-Ck Di 
29.49 0.34 0.12 0.05 1.22 14 22.75 0.33 0.26 0.20 0.76 
31.12 0.41 0.17 0.03 0.79 15 21.15 0.42 0.17 0.07 0.80 
20.65 0.45 0.30 0.12 0.77 16 20.38 0.40 0.26 0.15 0.02 
25.19 0.36 0.25 0.13 0.33 17 26.20 0.29 0.23 0.23 1.78 
30.95 0.36 0.14 0.07 0.84 18 14.50 0.37 0.13 0.15 1.57 
20.31 0.43 0.27 0.14 0.32 19 15.52 0.41 0.26 0.16 0.09 
27.95 0.44 0.34 0.28 1.38 20 20.88 0.32 0.22 0.34 3.06 
26.85 0.35 0.24 0.05 1.56 21 13.42 0.41 0.26 0.13 0.13 
20.77 0.42 0.28 0.05 1.11 22 19.41 0.40 0.38 0.25 1.42 
10 22.20 0.41 0.30 0.26 0.68 23 17.76 0.40 0.20 0.12 0.27 
11 20.92 0.35 0.30 0.21 0.90 24 19.45 0.44 0.32 0.30 1.75 
12 20.61 0.37 0.31 0.14 1.31 25 23.95 0.46 0.26 0.13 1.04 
13 29.53 0.34 0.14 0.06 1.05 26 18.26 0.44 0.20 0.04 1.03 
ID Mean L-Cv L-Cs L-Ck Di ID Mean L-Cv L-Cs L-Ck Di 
29.49 0.34 0.12 0.05 1.22 14 22.75 0.33 0.26 0.20 0.76 
31.12 0.41 0.17 0.03 0.79 15 21.15 0.42 0.17 0.07 0.80 
20.65 0.45 0.30 0.12 0.77 16 20.38 0.40 0.26 0.15 0.02 
25.19 0.36 0.25 0.13 0.33 17 26.20 0.29 0.23 0.23 1.78 
30.95 0.36 0.14 0.07 0.84 18 14.50 0.37 0.13 0.15 1.57 
20.31 0.43 0.27 0.14 0.32 19 15.52 0.41 0.26 0.16 0.09 
27.95 0.44 0.34 0.28 1.38 20 20.88 0.32 0.22 0.34 3.06 
26.85 0.35 0.24 0.05 1.56 21 13.42 0.41 0.26 0.13 0.13 
20.77 0.42 0.28 0.05 1.11 22 19.41 0.40 0.38 0.25 1.42 
10 22.20 0.41 0.30 0.26 0.68 23 17.76 0.40 0.20 0.12 0.27 
11 20.92 0.35 0.30 0.21 0.90 24 19.45 0.44 0.32 0.30 1.75 
12 20.61 0.37 0.31 0.14 1.31 25 23.95 0.46 0.26 0.13 1.04 
13 29.53 0.34 0.14 0.06 1.05 26 18.26 0.44 0.20 0.04 1.03 
Figure 2

Spatial distribution of L-moment ratios.

Figure 2

Spatial distribution of L-moment ratios.

Sub-regionalization of sites based on L-Cs

The rainfall station sites are sub-divided into three sub-regions based on L-Cs values as ‘low’ L-Cs that ranges from 0.1 up to 0.2, ‘moderate’ L-Cs from 0.2 up to 0.3, and finally, ‘high’ L-Cs from 0.3 up to 0.4. It is found that sub-region A consists of 8 sites, sub-region B of 11 sites, while sub-region C has 7 sites. Figure 3 shows the relationship between L-Cs and L-Cv for each site in the three sub-regions, while Table 2 presents the Di for each site in the three sub-regions. It is observed that the Di values for each sub-region are less than the critical values, which is an indication that the three sub-regions can be considered as non-discordant. Figure 4 demonstrates the site location for each sub-region and the spatial distribution of Di.

Table 2

Discordancy measure (Di) for each site of the three sub-regions

Sub-region A Station J109 J110 J116 M102 M108 M111 M204 W109    
Di 0.833 0.501 0.204 1.254 0.456 1.896 1.906 0.950    
Sub-region B Station J112 J117 J133 J140 M103 M109 M110 M112 M113 M116 W106 
Di 0.192 0.695 2.324 0.780 1.564 0.052 0.999 0.288 2.206 0.115 1.785 
Sub-region C Station J111 J118 M001 M004 M101 M117 M205     
Di 1.742 0.445 0.497 1.177 0.757 1.688 0.693     
Sub-region A Station J109 J110 J116 M102 M108 M111 M204 W109    
Di 0.833 0.501 0.204 1.254 0.456 1.896 1.906 0.950    
Sub-region B Station J112 J117 J133 J140 M103 M109 M110 M112 M113 M116 W106 
Di 0.192 0.695 2.324 0.780 1.564 0.052 0.999 0.288 2.206 0.115 1.785 
Sub-region C Station J111 J118 M001 M004 M101 M117 M205     
Di 1.742 0.445 0.497 1.177 0.757 1.688 0.693     
Figure 3

Relationship between L-Cs and L-Cv for the three sub-regions.

Figure 3

Relationship between L-Cs and L-Cv for the three sub-regions.

Homogeneity tests (H)

The computed L-moment ratios in Table 1 are used to calculate the regional average L-moment ratios, which are given in Table 3. It can be noticed that the regional average L-moment ratios for sub-region A are the lowest and for sub-region C are the highest. These regional average L-moment ratios are then used in homogeneity tests (H).

Table 3

Computed regional average L-moment ratios for each sub-region

Sub-region       
0.3816 0.1555 0.0695 
0.3817 0.2530 0.1548 
0.4079 0.3210 0.2249 
Sub-region       
0.3816 0.1555 0.0695 
0.3817 0.2530 0.1548 
0.4079 0.3210 0.2249 

Homogeneity tests (H1, H2, and H3) are computed based on regional weighted average L-moments and the simulation of kappa distribution. The results are presented in Table 4 for the three homogeneity tests over the three sub-regions, where all three tests indicate that these sub-regions are ‘acceptably homogenous’ except H1 test for sub-region B, which is ‘possibly homogenous’.

Table 4

Homogeneity tests (H) for the three sub-regions

  Sub-region A
 
Sub-region B
 
Sub-region C
 
H1 0.401 Acceptably homogenous 1.545 Possibly homogenous −0.665 Acceptably homogenous 
H2 −1.014 Acceptably homogenous −1.652 Acceptably homogenous −1.937 Acceptably homogenous 
H3 −1.660 Acceptably homogenous −1.781 Acceptably homogenous −1.354 Acceptably homogenous 
  Sub-region A
 
Sub-region B
 
Sub-region C
 
H1 0.401 Acceptably homogenous 1.545 Possibly homogenous −0.665 Acceptably homogenous 
H2 −1.014 Acceptably homogenous −1.652 Acceptably homogenous −1.937 Acceptably homogenous 
H3 −1.660 Acceptably homogenous −1.781 Acceptably homogenous −1.354 Acceptably homogenous 

Goodness of fit test (Zdist)

Five three-parameters PDFs are evaluated using Zdist test, which are generalized logistic (GLO), generalized extreme value (GEV), generalized normal (GNO), generalized Pareto (GPA), and Pearson type III (PE3). It is noticed that for sub-region A, GPA is the best fit among the others; for sub-region B, three PDFs, GEV, GNO, and PE3 fit well, and for sub-region C another three PDFs, GEV, GLO, and GNO fit well. Table 5 includes the computed values for the three sub-regions.

Table 5

The computed values of |ZDist | for the three sub-regions

  
GEV 4.528 1.501 0.212 
GLO 6.983 2.994 0.512 
GNO 4.338 0.769 0.910 
GPA 0.814 2.267 2.289 
PE3 3.672 0.553 2.125 
  
GEV 4.528 1.501 0.212 
GLO 6.983 2.994 0.512 
GNO 4.338 0.769 0.910 
GPA 0.814 2.267 2.289 
PE3 3.672 0.553 2.125 

L-moment ratio diagram (LMRD)

L-moment ratio diagrams (LMRDs) are developed for the three sub-regions to select the overall best PDF. For sub-region A, GPA is the best, whereas for sub-region B, it is PE3 and for sub-region C, GEV PDF. Figure 5 presents the LMRD for each sub-region.

Figure 4

Site locations for the three sub-regions (left) and Di spatial distribution (right).

Figure 4

Site locations for the three sub-regions (left) and Di spatial distribution (right).

Regional growth curve development

Regional average L-moment ratio calculations in Table 3 help to estimate each candidate PDF parameters, then the regional quantiles are computed for each sub-region, which are already provided in Table 6 and Figure 6 for the regional growth curves in each sub-region. It can be noticed that as for high probability of non-exceedance (0.90), sub-region A has the lowest quantiles with low increase, while sub-region C has the highest quantiles with steep increase.

Table 6

Regional quantiles for different probabilities for each sub-region

Probability of non-exceedance Return period (yr) Sub regions
 
0.98 50 2.55 3.00 3.45 
0.99 100 2.68 3.43 4.27 
0.995 200 2.78 3.86 5.23 
0.998 500 2.87 4.41 6.74 
0.999 1,000 2.91 4.83 8.10 
Probability of non-exceedance Return period (yr) Sub regions
 
0.98 50 2.55 3.00 3.45 
0.99 100 2.68 3.43 4.27 
0.995 200 2.78 3.86 5.23 
0.998 500 2.87 4.41 6.74 
0.999 1,000 2.91 4.83 8.10 
Figure 5

L-moment ratio diagram for each sub-region A, B, and C.

Figure 5

L-moment ratio diagram for each sub-region A, B, and C.

Figure 6

Regional growth curve for each sub-region.

Figure 6

Regional growth curve for each sub-region.

Quantiles estimates

Regional growth curves developed from the previous section are used to compute the quantiles for each station in the three sub-regions for a 100-year return period (0.99 probability of non-exceedance). Predicted rainfall depth for a 100-year return period ranges from 38.8 mm in the north and north-east to 119 mm in the south and south-east with an average of 75.9 mm. Figure 7 shows the spatial distribution of 100-year rainfall depth.

Figure 7

Spatial distribution of rainfall depth for 100 years' return periods.

Figure 7

Spatial distribution of rainfall depth for 100 years' return periods.

Climate change impact

The PME used PRECIS climate model to simulate the climate change at the end of the 21st century over KSA using several emission scenarios. Herein, A2 scenario is selected, which indicates 40% increase in rainfall (Al Zawad & Aksakal 2010). This percentage is implemented in the extreme rainfall depth 100-year return period prediction for each station. Figure 8 shows the spatial distribution of 100-year return period rainfall predictions by taking into consideration the climate change effects. It can be noticed that the southern part receives heavy to moderate rainfall, while the northern part experiences lighter rainfall. This extreme rainfall spatial distribution is very helpful for the practitioners in water resources projects planning, design, operation and maintenance.

Figure 8

The spatial distribution of predicted extreme rainfall of 100-year return period taking into consideration the climate change effects.

Figure 8

The spatial distribution of predicted extreme rainfall of 100-year return period taking into consideration the climate change effects.

CONCLUSIONS

In the present paper, the rainfall data from 26 sites in the western KSA are analyzed for extreme rainfall prediction over the study area, 180,000 km2. The study region is sub-divided into three non-discordant sub-regions based on L-Cs values, while homogeneity tests (H1, H2, and H3) indicate that the three sub-regions are ‘acceptably homogenous’. Goodness of fit test Zdist helps to evaluate five three-parameters' PDFs. It is found that for sub-region A, GPA fits the best among the others, for sub-region B, three PDFs are valid, which are GEV, GNO, and PE3, and for sub-region C another three PDFs, GEV, GLO, and GNO fit. L-moment ratio diagrams (LMRDs) are then developed for the three sub-regions to select the overall best fit PDF. For sub-region A, GPA is the best, for sub-region B, PE3 and for sub-region C, GEV. Subsequently, the regional growth curve is developed for each sub-region. Results show that for high probability of non-exceedance (0.90), sub-region A has the lowest quantiles with smooth increase, while sub-region C has the highest with steep increase. The rainfall prediction for 100-year return period is then computed for each station and the rainfall climate change effects using A2 emission scenario are simulated and implemented in the computation of extreme rainfall frequency prediction. The results of this study are expected to be very beneficial for flood studies, especially in ungauged areas.

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Author notes

Deceased.