This study investigated the rainfall patterns, spatial variability, surface runoff generation and dam requirements in the southwestern region of Saudi Arabia. The region was divided into four areas Asir, Jazan, Al-Baha and the Red Sea Coast. Surface runoff was estimated for eight scenarios considering the runoff coefficients of 0.05–0.70, resulting in 203–2,835 million cubic meters (MCM) of runoff per year in this region. The runoff in the Asir, Jazan, Al-Baha and the Red Sea Coast were estimated to be in the ranges of 88–1,230, 53–738, 32–443 and 30–425 MCM per year, respectively. The capacities of the existing dams in Asir, Jazan and Al-Baha are approximately 373, 194 and 31 MCM, respectively, while the coast does not have any dam. A significant fraction of runoff is likely to be lost in each scenario of assessment. Water resources may be augmented through construction of new dams and/or wells in appropriate locations. However, better understanding is advisable on locations, water availability, surface evaporation in wadies and reservoirs, accumulation of solids in dam/reservoirs, hydraulic conductivity, economic burdens and national policy.

## INTRODUCTION

The Kingdom of Saudi Arabia is located in an arid region, which has low average annual rainfall (FAO 2009; Chowdhury & Al-Zahrani 2013a). The population has increased several fold since 1972, resulting in a significant increase of water use (CIA 2011). The total water consumption in 2000, 2004 and 2009 was 20,740, 20,270 and 18,507 million cubic meters (MCM), respectively. The agricultural water demand in these years was 18,540, 17,530 and 15,464 MCM, respectively. The domestic water demand was 1,750, 2,100 and 2,330 MCM, respectively, while the industrial water demand was 450, 640 and 713 MCM in these years, respectively (MOEP 2010). Water demands in the kingdom are satisfied by non-renewable groundwater sources (NGW), renewable surface and groundwater sources (RGSW), desalinated water (DW) and treated wastewater (TWW), in which the NGW supplies the most followed by the RGSW, DW and TWW (MOEP 2010). Approximately 13,490 and 11,551 MCM of water was supplied from the NGW in 2004 and 2009, respectively (MOEP 2010). Water supplies from RGSW were 5,410 and 5,541 MCM in 2004 and 2009, respectively. The desalination plants supplied 1,070 and 1,048 MCM of DW in 2004 and 2009, respectively, while TWW reuse was increased from 260 to 325 MCM during this period (MOEP 2010). However, the data from the Ministry of Water and Electricity (MOWE) showed considerable differences. The MOWE reported that the GW extraction in 2009, 2010, 2011 and 2012 was 16,842, 16,110, 15,408 and 14,999 MCM, respectively (MOWE 2013). The variability was also noted for wastewater generation and reuse, supplies of DW, and dams and surface water supplies (MOWE 2013).

In an earlier study, the Ministry of Water (MAW) of Saudi Arabia [currently, MOWE] reported that the proven, probable and possible groundwater reserves in the non-renewable aquifers were approximately 259, 416 and 761 billion cubic meters (BCM), respectively (MAW 1984; Water Atlas 1995; FAO 1998). FAO (1998) reported that approximately 42% of the reserves might have been consumed by 1996. The total surface runoff was estimated to be 2.2 BCM/year (FAO 2009), most of which infiltrates to recharge the shallow aquifers. In 2012, a total of 449 dams in the country stored and recharged approximately 2.02 BCM of runoff (MOWE 2013), which is significantly higher than the MOEP data, which reported 302 dams collecting approximately 1.4 BCM of runoff in 2009 (MOEP 2010). The water reserves and withdrawal rates indicate that the available resources may not be enough to provide support on a long-term basis (MAW 1984; Water Atlas 1995; FAO 1998; Chowdhury & Al-Zahrani 2013a). It is advisable to find new resources of water and conserve NGW (MOEP 2010).

Harvesting of rainwater from the regions with higher rainfall may provide significant support for water resources management. Rainwater harvesting has been practised since 4500 bc. Different approaches were adopted to collect and use surface runoff in the Arabian region. In Yemen, rainwater was collected and stored through channels and dams in 1700 bc. In the Negev desert to the north of the Arabian Peninsula, rainwater was collected for domestic and agricultural uses about 4000 years ago (Evenari 1961; Sivanappan 2006). It is economically feasible and known as a potential alternative to water resources in the arid regions (Yuan et al. 2002). In Saudi Arabia, the source of surface water is the seasonal precipitation. The country has an overall average annual rainfall of approximately 125 mm (Chowdhury & Al-Zahrani 2013a). In the north, annual rainfall varies between <100 and 200 mm (long-term average = 70.1 mm/year), while in the south, 500 mm/year of rainfall (long-term average = 265 mm/year) is not unlikely (FAO 2009). The largest runoff occurs in the western region, which represents approximately 60% of the total runoff although it covers only 10% of the land area (FAO 2009). The remaining 40% of the runoff occurs in the far south of the western coast (Tahama), which covers 2% of the land area (FAO 2009). The MOWE data revealed that 89 dams in the southwestern (SW) region collected approximately 600 MCM/year of water (MOWE 2011). Some of the major dams are King Fahd dam in the Asir region (capacity: 325 MCM), Wadi Abha in the Asir region (capacity: 213 MCM) and Bish dam in Jizan (capacity: 193.6 MCM). However, the yearly rainfall data indicate that the possible surface runoff might be significantly higher than the currently collected runoff. The floods in the SW regions in 2009, 2011 and 2013 were responsible for 100, 10 and seven deaths, respectively (BBC News 2009; CNN World 2011; Arab News 2013), which indicated that the runoff might be higher than the capacities of the dams, and/or the drainage systems are vulnerable.

In this study, rainfall patterns and spatial variability in the SW region (e.g., Asir, Jazan, Al-Baha and the Red Sea Coast) were investigated. The surface runoff was quantified at various scenarios of runoff coefficients. The current capacities of the dams were compared with the runoff. The additional capacities of the dams needed to store the excess runoff were estimated. Finally, the policy-related issues and benefits of collecting the excess runoff were highlighted.

## METHODOLOGY

### Study area

The SW region of Saudi Arabia is mountainous with elevations exceeding 2,000 m above the mean sea level. The region lies within the subtropical climate zone and receives the highest rainfall in the country (Al-Subyani 2004; FAO 2009). The location of the study region is shown in Figure 1. It includes Al-Baha (north part), Asir (center), Jazan (south) and the Red Sea Coast (west). It covers approximately 57,394 km2 of land area. The study region was divided into four areas Asir, Jazan, Al-Baha and the Red Sea Coast (Figure 1). The Asir region falls under the influence of a relatively moist south-easterly stream of monsoon air (Al-Subyani 2004). The periods of March–May and July–August are the main rainy seasons, possibly due to an increase in rainfall along the leeward side of the mountains and the Red Sea Coast. In Al-Baha, the rainy periods are the spring months (March–May), while rainfall is low for the rest of the year. In Jazan and the Red Sea Coast, the rainy periods are July–November and April–May.

Figure 1

Area of study in the south-western region of Saudi Arabia.

Figure 1

Area of study in the south-western region of Saudi Arabia.

### Selecting method of analysis

Rainfall is generally measured by rain gauges and radar-based remote sensing (Maliva & Missimer 2012). Rain gauges provide point measurements of rainfall, which have several limitations, while the long-term records may provide satisfactory levels of accuracy. In contrast, the radar measurement of rainfall can provide data over large areas, which is more useful for evaluation of catchment or basin-wide water budgets (Maliva & Missimer 2012). In this study, long-term rain gauge data (1965–2010) were available for the SW region. The SW region is a highly complex area in terms of terrain and rainfall distribution. The region contains mountains, valleys, gullies, wadies, plains, lowlands and the Red Sea Coast. To estimate the rainfall distribution, monthly average data were collected from the monitoring stations for 45 years (1965–2010). Several techniques are used to predict rainfall distributions (Al-Subyani 2004). The Thiessen polygon method is one of the classical techniques for characterizing spatial distribution of rainfall. This method divides the study area into polygons of influence. Each polygon contains a rainfall station in its centroid and the rainfall records of that station are assigned to the polygon. The polygon boundaries are determined based on the distances between the rainfall monitoring stations (Isaaks & Srivastava 1989). This method is still used in estimating average distribution of precipitation (e.g., Li et al. 2009). The polynomial interpolation is another classical technique used for estimating the spatial distribution of rainfall. This technique develops a linear or non-linear polynomial relationship for estimating rainfall based on the locations of rainfall stations (Hwang et al. 2012). The inverse distance weighted (IDW) method is widely used in hydrological and climate change studies (Chen et al. 2010; Hwang et al. 2012). This technique depends on the distance between rainfall stations to develop a relationship for predicting rainfall in the un-gagged locations. The nearest un-gagged locations from the existing stations are given the highest weight, while the farthest has the lowest weight (Isaaks & Srivastava 1989; Chen et al. 2010).

The classical estimation and interpolation methods simplify the rainfall estimates. Such simplifications often encounter disadvantages, which may be misleading and/or reduce the accuracy of rainfall distribution, particularly in arid regions where spatial variation is extreme. Averaging methods, such as arithmetic, harmonic and geometric methods, are simple techniques to deal with the highly complex terrain and hydrological aspects. Polygon techniques, such as Thiessen and triangulation, produce a discontinuous rainfall distribution between the sub-areas. This discontinuity depends on several factors, such as the size of the sub-areas, rainfall variations and the averaging process. Conventional polynomial techniques build their estimations based on the locations in space of known rainfall stations without considering the topography. This is an important drawback, especially when strong orographic and elevation effect are anticipated (Hwang et al. 2012). The IDW method estimates rainfall at a specific location as a block. The estimation is based on the distance between the centroids of stations. As such, the size of the block does not show any difference to the estimations.

The geostatistical techniques incorporate spatial distribution of rainfall stations, which increases the accuracy of rainfall distributions. The drawbacks of conventional techniques can be greatly reduced in these techniques (Isaaks & Srivastava 1989). These techniques are frequently used in estimating rainfall distributions (Haberlandt 2007; Murthy & Abbaiah 2007; Cheng et al. 2008). Kriging and Co-Kriging have been widely used by hydrologists and climatologists to show spatial distribution of rainfall. The Kriging results in unbiased estimations with reduced variance (Webster & Oliver 2000). It uses the weighted linear combinations of data, minimizes the mean errors and tries to reduce the variance errors (Isaaks & Srivastava 1989).

### Kriging and Co-Kriging methods

In the Kriging method, the rainfall at any un-gauged location can be estimated by adding a random error parameter to the mean rainfall in that region (Al-Subyani 2004). This can be expressed as
1
where Z = rainfall in the un-gauged location; x =coordinate of the location; μ =overall mean rainfall; and ɛ =random error with spatial dependence. Kriging calculates the rainfall at unknown locations by using the available data. It incorporates the spatial distribution of gauged and un-gauged locations and assigns weight to each location to control its effect on the un-gauged locations (Isaaks & Srivastava 1989). It can be shown as
2
where Z(xi) = the measured rainfall for the ith point; Z(xo) = the estimated rainfall at a specific location; and λi = the linear weight for the measured rainfall at the ith point. The values of the weights (λi) are spatially dependent on the locations of the measured rainfall data. These are the functions of the semivariogram and mean. These weights can be determined through simultaneous solution of linear equations as
3

4
where λi = weight at point i; λj = weight at point j; μ = overall mean; = semivariogram between points xi and xj; and = semivariogram between points i and its location. Semivariogram is a function that shows the degree of spatial dependence of Z(x). It is defined as the variance of the difference of field values at two locations across realizations of the field (Cressie 1993). Semivariogram is defined as:
5
where n = number of pairs; x and x + h =sampling locations at direction x separated by distance h; and Z =measured values for rainfall at the corresponding locations. Co-Kriging is a modified form of Kriging with similar concepts. The main difference is the use of two variables (e.g., rainfall and altitude) in the estimation process in Co-Kriging compared to one variable used in Kriging (rainfall). Rainfall is considered as the primary variable and the secondary variable must be spatially correlated with the primary variable (Isaaks & Srivastava 1989). Unlike Kriging, Co-Kriging has three semivariograms, one for each of the primary and secondary variables and a cross semivariogram for both variables as
6

7

8

9
where M = primary variable; c = secondary variable; xi = ith point location for the primary variable; xo = estimated value at specific location for the primary variable; yj = jth point location for the secondary variable; λi = weight for the measured value at the ith point location for the primary variable; and νj = weight for the measured value at the ith point location for the secondary variable. Co-Kriging was reported to have shown a better estimation of rainfall distribution compared to other geostatistical techniques (Hevesi et al. 1992). In this paper, Co-Kriging was used to estimate the distribution of the rainfall over the SW region using rainfall records as the main variable and the elevation of the rainfall stations as an auxiliary variable. Based on the rainfall contour maps, it is possible to estimate the monthly and annual rainfall volume in these regions. Further details on Kriging and Co-Kriging can be found elsewhere (Isaaks & Srivastava 1989; Hevesi et al. 1992; Cressie 1993).

## RESULTS

### Statistical distributions for rainfall

The rainfall distributions over the SW region showed tempospatial variability. The monthly rainfall data for the period of 45 years (1965–2010) in the Asir, Jazan, Al-Baha and the Red Sea Coast mainly followed the Gamma, LogNormal (LN) and Weibull distributions. Tables 14 show the statistical distributions of monthly rainfall for different areas. In Asir, average rainfall in July followed Normal distribution, while the monthly rainfall for all other months in each area followed the LN, Weibull, Gamma or largest extreme value distributions, indicating that the rainfall mostly followed the skewed patterns (Tables 14). The coefficient of variation (CV = std dev/mean) of the rainfall showed high values (Asir: 0.50–2.54; Al-Baha: 1.1–4.48; Jazan: 0.72–1.83; and Red Sea Coast: 0.56–1.42), meaning that these data had very wide ranges (Tables 14). The skewness coefficients for the rainfall in Asir, Al-Baha, Jazan and the Red Sea Coast had the ranges of −0.03–9.11, 2.12–24.7, 1.81–7.79 and 1.59–4.69, respectively. The skewness coefficient of zero indicates that the data are symmetric, the negative value indicates that the tail on the left side of the curve is longer than the right side, while the positive value indicates that the tail on the right side is longer than the left side, and the bulk of the values lie to the left of the mean value (Montgomery & Runger 2007). The higher values of CV, high positive skewness coefficients and skewed distributions in Tables 14 demonstrate that the rainfall in some months was much higher than the averages of monthly rainfall in these areas.

Table 1

Monthly rainfall distributions for Asir (mm)

Month Distribution Average CV (%) Skewness
January Gamma (0.62, 15.47) 9.81 125.7 2.71
February Gamma (0.48, 18.75, 0.086) 8.98 145.4 3.19
March Gamma (0.68, 29.29) 20.22 120.0 2.47
April W (1.09, 31.93, 4.3) 35.26 81.03 1.91
May LEV (17.81, 16.1) 27.0 76.3 1.10
June W (1.0, 5.07, 0.07) 5.1 99.24 1.97
July N (8.93, 5.16) 8.9 58.55 -0.03
August LN (2.79, 0.47, 0) 18.19 49.37 1.65
September Gamma (0.77, 4.31, 0.04) 3.45 113.4 2.21
October W (0.64, 3.48) 4.85 161.6 3.76
November LN (1.05, 1.57) 9.43 253.7 9.11
December W (0.73, 4.62) 5.69 132.5 2.67
Month Distribution Average CV (%) Skewness
January Gamma (0.62, 15.47) 9.81 125.7 2.71
February Gamma (0.48, 18.75, 0.086) 8.98 145.4 3.19
March Gamma (0.68, 29.29) 20.22 120.0 2.47
April W (1.09, 31.93, 4.3) 35.26 81.03 1.91
May LEV (17.81, 16.1) 27.0 76.3 1.10
June W (1.0, 5.07, 0.07) 5.1 99.24 1.97
July N (8.93, 5.16) 8.9 58.55 -0.03
August LN (2.79, 0.47, 0) 18.19 49.37 1.65
September Gamma (0.77, 4.31, 0.04) 3.45 113.4 2.21
October W (0.64, 3.48) 4.85 161.6 3.76
November LN (1.05, 1.57) 9.43 253.7 9.11
December W (0.73, 4.62) 5.69 132.5 2.67

W: Weibull; LN, LogNormal; LEV: largest extreme value; N: normal (for W, LN, LEV and Gamma distributions: 1st parameter = shape factor; 2nd parameter = location; 3rd parameter: threshold value). For the normal distribution [1st parameter: mean; and 2nd parameter: standard deviation]; CV: coefficient of variation.

Table 2

Monthly rainfall distributions for Al-Baha (mm)

Month Distribution Average CV (%) Skewness
January Gamma (0.70, 11.69) 8.36 119.8 2.38
February Gamma (0.70, 8.96) 6.29 120.1 2.56
March Gamma (0.72, 17.2, 0.29) 12.78 115.1 2.59
April LN (2.71, 0.93, 0) 23.22 117.4 5.0
May Gamma (0.82, 12.47) 10.11 110.0 2.12
June Gamma (0.85, 3.13) 2.67 108.0 2.23
July W (0.76, 1.71, 0.002) 2.04 135.7 3.27
August LN (0.26, 1.65, 0.02) 5.48 386.8 23.0
September LN (-1.36, 1.21, 0.01) 0.54 181.2 7.22
October LN (-0.016, 1.79) 5.04 448.1 24.7
November Gamma (0.71, 5.77) 4.1 119.1 2.38
December Gamma (0.80,6.06) 4.85 113.2 2.23
Month Distribution Average CV (%) Skewness
January Gamma (0.70, 11.69) 8.36 119.8 2.38
February Gamma (0.70, 8.96) 6.29 120.1 2.56
March Gamma (0.72, 17.2, 0.29) 12.78 115.1 2.59
April LN (2.71, 0.93, 0) 23.22 117.4 5.0
May Gamma (0.82, 12.47) 10.11 110.0 2.12
June Gamma (0.85, 3.13) 2.67 108.0 2.23
July W (0.76, 1.71, 0.002) 2.04 135.7 3.27
August LN (0.26, 1.65, 0.02) 5.48 386.8 23.0
September LN (-1.36, 1.21, 0.01) 0.54 181.2 7.22
October LN (-0.016, 1.79) 5.04 448.1 24.7
November Gamma (0.71, 5.77) 4.1 119.1 2.38
December Gamma (0.80,6.06) 4.85 113.2 2.23

W: Weibull; LN: LogNormal; Gamma [1st parameter = shape factor, 2nd parameter = location; 3rd parameter: threshold value].

Table 3

Monthly rainfall distributions for Jazan (mm)

Month Distribution Average CV (%) Skewness
January Gamma (0.99, 18.12) 17.6 103.3 2.13
February Gamma (1.0, 10.22) 10.2 98.8 1.93
March Gamma (0.69, 18.27, 0.44) 12.9 116.5 2.29
April W (0.98, 28.11) 28.5 101.5 1.95
May W (1.11, 21.96,0) 21.3 92.6 1.81
June LN (2.67, 0.7, 0) 18.7 79.0 2.71
July LN (2.90, 1.26) 39.2 183.1 7.79
August LN (3.71, 0.68,0) 51.7 77.7 2.86
September LN (3.23, 0.65,0) 31.2 72.2 2.34
October W (1.25, 21.17) 19.7 79.8 1.32
November W (1.21, 25.11, 0) 23.4 82.1 1.45
December LN (2.78, 0.96) 25.6 117.9 3.73
Month Distribution Average CV (%) Skewness
January Gamma (0.99, 18.12) 17.6 103.3 2.13
February Gamma (1.0, 10.22) 10.2 98.8 1.93
March Gamma (0.69, 18.27, 0.44) 12.9 116.5 2.29
April W (0.98, 28.11) 28.5 101.5 1.95
May W (1.11, 21.96,0) 21.3 92.6 1.81
June LN (2.67, 0.7, 0) 18.7 79.0 2.71
July LN (2.90, 1.26) 39.2 183.1 7.79
August LN (3.71, 0.68,0) 51.7 77.7 2.86
September LN (3.23, 0.65,0) 31.2 72.2 2.34
October W (1.25, 21.17) 19.7 79.8 1.32
November W (1.21, 25.11, 0) 23.4 82.1 1.45
December LN (2.78, 0.96) 25.6 117.9 3.73

W: Weibull; LN: LogNormal; Gamma [1st parameter = shape factor, 2nd parameter = location; 3rd parameter: threshold value].

Table 4

Monthly rainfall distributions for the Red Sea Coast (mm)

Month Distribution Average CV (%) Skewness
January Gamma (0.79, 13.06) 10.0 114.9 2.42
February Gamma (0.48, 11.5, 0.06) 5.7 141.5 2.87
March W (0.83, 7.85, 0.11) 8.7 118.2 2.47
April LN (2.04, 1.0, 0.11) 12.9 125.8 4.69
May W (1.12, 12.75, 0.36) 12.8 86.3 1.65
June LN (2.40, 0.56, 0) 12.8 58.3 1.82
July Gamma (1.55, 6.94) 10.7 79.4 1.59
August LN (2.89, 0.57, 0) 20.7 60.4 1.66
September LN (2.98, 0.53, 0) 22.6 56.0 1.79
October LN (2.67, 0.85, 0) 21.2 107.4 4.37
November Gamma (1.33, 8.0) 10.7 87.4 1.72
December W (0.96, 8.27, 0.28) 8.9 97.8 1.98
Month Distribution Average CV (%) Skewness
January Gamma (0.79, 13.06) 10.0 114.9 2.42
February Gamma (0.48, 11.5, 0.06) 5.7 141.5 2.87
March W (0.83, 7.85, 0.11) 8.7 118.2 2.47
April LN (2.04, 1.0, 0.11) 12.9 125.8 4.69
May W (1.12, 12.75, 0.36) 12.8 86.3 1.65
June LN (2.40, 0.56, 0) 12.8 58.3 1.82
July Gamma (1.55, 6.94) 10.7 79.4 1.59
August LN (2.89, 0.57, 0) 20.7 60.4 1.66
September LN (2.98, 0.53, 0) 22.6 56.0 1.79
October LN (2.67, 0.85, 0) 21.2 107.4 4.37
November Gamma (1.33, 8.0) 10.7 87.4 1.72
December W (0.96, 8.27, 0.28) 8.9 97.8 1.98

W: Weibull; LN: LogNormal; Gamma [1st parameter = shape factor; 2nd parameter = location; 3rd parameter: threshold value].

The yearly average rainfall in these areas was investigated for calculating the exceedance probabilities. The cumulative distribution functions (CDFs) for the yearly average rainfall in Asir, Al-Baha, Jazan, the Red Sea Coast and the entire region (Asir, Al-Baha, Jazan and the Red Sea Coast in combination) are presented in Figure 2. The 50-percentile rainfall for Asir, Al-Baha, Jazan, the Red Sea Coast and the entire region were 151.8, 74.6, 266, 143 and 162.2 mm, respectively (Figure 2). The 50-percentile rainfall in Asir, Jazan and the Red Sea Coast were much higher than the average yearly rainfall of the country. Figure 2 shows that the probabilities of exceeding the rainfall of 250 mm/year were 0.063, 0.004, 0.575, 0.133 and 0.011 for Asir, Al-Baha, Jazan, the Red Sea Coast and the entire region, respectively. The annual average rainfall in Asir, Al-Baha, Jazan, Red Sea Coast and the entire region exceeded 400 mm/year by the exceedance probabilities of 0.001, 0.00, 0.108, 0.02 and 0.00, respectively. Among these four areas, the rainfall exceeded the value of 500 mm/year in Jazan and the Red Sea Coast by the probabilities of 0.028 and 0.006, respectively. Figure 2 demonstrates that the highest annual rainfall were recorded for Jazan followed by the Red Sea Coast and Asir, while the lowest average rainfall was recorded for Al-Baha. Further details on the exceedance probabilities for different cutoff values are presented in Table 5. The data in Table 5 and Figure 2 indicate that there might be high potential of harvesting surface runoff from Asir, Al-Baha, Jazan and the Red Sea Coast.

Table 5

Regional rainfall exceedance probability (rainfall per year)

Area 100 mm 200 mm 250 mm 300 mm 350 mm 400 mm 450 mm
Asir 0.9 0.199 0.063 0.018 0.005 0.001 0.00
Baha 0.258 0.014 0.004 0.001 0.00 0.00 0.00
Jazan 0.999 0.807 0.575 0.358 0.207 0.108 0.055
Coast 0.764 0.252 0.133 0.07 0.037 0.02 0.0011
Total 0.995 0.133 0.011 0.005 0.001 0.00 0.00
Area 100 mm 200 mm 250 mm 300 mm 350 mm 400 mm 450 mm
Asir 0.9 0.199 0.063 0.018 0.005 0.001 0.00
Baha 0.258 0.014 0.004 0.001 0.00 0.00 0.00
Jazan 0.999 0.807 0.575 0.358 0.207 0.108 0.055
Coast 0.764 0.252 0.133 0.07 0.037 0.02 0.0011
Total 0.995 0.133 0.011 0.005 0.001 0.00 0.00
Figure 2

Determination of probabilities of exceedance of yearly average rainfall in the south-western region (Y axis represents cumulative probability; X axis represents rainfall: mm/yr).

Figure 2

Determination of probabilities of exceedance of yearly average rainfall in the south-western region (Y axis represents cumulative probability; X axis represents rainfall: mm/yr).

### Correlations between rainfall and elevation

In the Co-Kriging technique, the coefficient of determination (R2) and correlation coefficients (r) for the cross-validation plots of rainfall data and elevations of stations were in the range of 0.77–0.99 and 0.877–0.995, respectively. The high values of correlation coefficients (r) demonstrate strong relationships between the rainfall records (main parameter) and the elevations of stations (auxiliary or secondary parameter). However, when other estimation techniques, such as Kriging and IDW were used, R2 for the cross-validation plots was in the ranges of 0.13–0.63 and 0.11–0.63, respectively. Figure 3 shows the comparison of R2 for the cross-validation plots in the Kriging, Co-Kriging and IDW methods. The Co-Kriging method presented better estimations for rainfall distributions at varying elevations of rain gauge stations. This method appears to be better than the Kriging and IDW methods (Figure 3). Between the Kriging and IDW methods, Kriging showed higher R2 from December to May, while the IDW method showed higher R2 from June to November. The strong correlations between rainfall and elevation demonstrate that the areas with higher elevations in the SW region may experience higher rainfall.

Figure 3

R2 for Kriging, Co-Kriging and IDW methods.

Figure 3

R2 for Kriging, Co-Kriging and IDW methods.

### Rainfall quantity

The region under study covers an area of 157.59 × 364.2 km = 57,394 km2, with the latitude/longitude combinations of (186,773 m E, 1,877,164 m N) and (344,363 m E, 2,241,392 m N), respectively (Figures 46). The details of the region are shown in Figure 1. The rainfall contour maps (Figures 46) show that the entire region had significant amounts of rainfall. Figures 46 show that the rainfall in Jazan (bottom), Coast (left) and Asir (central) were much higher than Al-Baha (north), which is consistent with the CDF of the rainfall in these areas. Using the rainfall intensities from the contour maps (Figures 46) and their corresponding areas, total rainfall in these areas was calculated. April, May and August had the highest averages of rainfall all over the year, amounting to about 873, 566 and 488 MCM, respectively, of rainfall for the SW region. The total rainfall for the entire region was estimated to be 4.05 BCM per year. The monthly distributions of rainfall in different areas are presented in Figure 7. Asir had the largest amount of rainfall totaling approximately 1.76 BCM/year. The rainfall in Jazan, Al-Baha and Red Sea Coast were 1.05, 0.63 and 0.61 BCM per year, respectively. The cumulative rainfall in Asir was higher than the other areas in most months except September and October (Figure 7). Approximately 43.5% of the cumulative rainfall was from Asir. Jazan, Al-Baha and the Red Sea Coast contributed approximately 25.9%, 15.5% and 15.1%, respectively, of the cumulative rainfall. The rainfall intensities in Jazan were higher than Asir in most cases. However, for the cumulative rainfall, predicted using the contour maps in Figures 46 and the corresponding areas, it is shown that the Asir area had the largest amount of cumulative rainfall, due mainly to a larger land area than Jazan.

Figure 4

Monthly average rainfall distributions from January to April using Co-Kriging.

Figure 4

Monthly average rainfall distributions from January to April using Co-Kriging.

Figure 5

Monthly average rainfall distributions from May to August using Co-Kriging.

Figure 5

Monthly average rainfall distributions from May to August using Co-Kriging.

Figure 6

Monthly average rainfall distributions from September to December using Co-Kriging.

Figure 6

Monthly average rainfall distributions from September to December using Co-Kriging.

Figure 7

Monthly rainfall for the Baha, Red Sea Coast, Jazan and Asir areas.

Figure 7

Monthly rainfall for the Baha, Red Sea Coast, Jazan and Asir areas.

### Surface runoff and storage capacities

The MOWE reported that 89 dams are available to capture surface runoff in the SW region (MOWE 2011). Among these, 56 dams are used for storage, 14 for flood control, 13 for drinking water and six for irrigation purposes (Table 6). Most of the dams are located in Asir (60), followed by Al-Baha (26 dams) and Jazan (three dams), while no dam is available in the Red Sea Coast (MOWE 2011). The total capacity of the dams is about 600 MCM, in which 562, 1.9, 30.1 and 3.9 MCM are used for storage, irrigation, drinking and flood control, respectively (Table 6). The dams in Asir have the highest capacity (373 MCM), while Jazan and Al-Baha have the capacities of 194 MCM and 31 MCM, respectively (Table 6).

Table 6

Dams, their locations, type and capacities

Asir

Jazan

Baha

Coast

Total

No. Capacity No. Capacity No. Capacity No. Capacity No. Capacity
Storage 34 360.27 193.64 21 8.08 – – 56 561.99
Irrigation 0.99 0.43 0.50 – – 1.91
Drinking 12 7.59 22.5 – – 13 30.09
Control 11 3.79 0.14 – – 14 3.93
Total 60 372.64 194.07 26 31.23 – – 89 597.92
Asir

Jazan

Baha

Coast

Total

No. Capacity No. Capacity No. Capacity No. Capacity No. Capacity
Storage 34 360.27 193.64 21 8.08 – – 56 561.99
Irrigation 0.99 0.43 0.50 – – 1.91
Drinking 12 7.59 22.5 – – 13 30.09
Control 11 3.79 0.14 – – 14 3.93
Total 60 372.64 194.07 26 31.23 – – 89 597.92

To estimate the runoff, it was essential to understand the intensity–duration–frequency (IDF) curve and/or rainfall–runoff curve for each area. However, no established IDF curve was available for these areas. The study areas are mostly mountainous, consisting primarily of sedimentary rock, limestone, sandstone and shale, which have made these mountains impervious. The Asir Mountains are approximately 103,684 km2, running parallel to the Red Sea and extending from the Yemen border to Taif, Saudi Arabia. This study focused on the area of 57,394 km2 comprising mainly the mountains and valleys. It is likely that the surface runoff is generated within a few minutes of rainfall. The recent photograph of Arab News on ‘Flash flood’ (Arab News 2013) shared a similar view. There have been few examples of intense flow immediately after heavy rainfall. The intense flows in 2009, 2011 and 2013 were responsible for the death of 100, 10 and seven people, respectively, in the SW region (BBC News 2009; CNN World 2011; Arab News 2013). In the areas with similar geological structure, past studies used the runoff coefficients in the range of 0.05–0.65. For an area in the SW region, Nouh (1987) reported a runoff coefficient in the range of 0.133–0.185. Şen & Al-Suba (2002) estimated the runoff coefficients at Tihama, Asir in the range of 0.05–0.22. In the mountainous areas, some studies showed that runoff coefficient might reach 0.65 (Holko & Kostka 2008). In this study, a wide range of runoff coefficients, ranging from 0.05 to 0.70, was assumed for each area to have an understanding of the possible ranges of runoff generations. Eight runoff coefficients covering the lowest and highest reported values of runoff coefficients were assumed in this paper (Table 7). The runoff at different scenarios are presented in Table 7. It should be noted that the runoff coefficients reported in the earlier studies were for some specific areas, which may not be representative of the entire region. Further, the mountains may have much higher runoff coefficients than the wadies, valleys, empty lands and green fields. In addition, the travel time is highly dependent on the topography, and evaporation and infiltration can play an important role on the values of runoff coefficients. As such, values of runoff coefficients are likely to vary tempospatially. To incorporate such a wide range of uncertainty, this study considers eight discrete values of runoff coefficients. Upon availability of more reliable data, the results can be updated in future.

Table 7

Runoff generations and collections in the south-western regions under different scenarios (MCM/year)

Predicted runoff

Area Current storage Case I (C = 0.05) Case II (C = 0.1) Case III (C = 0.2) Case IV (C = 0.3) Case V (C = 0.4) Case VI (C = 0.5) Case VII (C = 0.6) Case VIII (C = 0.7)
Asir 373 88 176 351 527 703 878 1,054 1,230
Jazan 194 53 105 211 316 422 527 633 738
Baha 31 32 63 126 190 253 316 379 443
Red Sea Coast 30 61 121 182 243 303 364 425
Total 598 203 405 810 1,215 1,620 2,025 2,430 2,835
Predicted runoff

Area Current storage Case I (C = 0.05) Case II (C = 0.1) Case III (C = 0.2) Case IV (C = 0.3) Case V (C = 0.4) Case VI (C = 0.5) Case VII (C = 0.6) Case VIII (C = 0.7)
Asir 373 88 176 351 527 703 878 1,054 1,230
Jazan 194 53 105 211 316 422 527 633 738
Baha 31 32 63 126 190 253 316 379 443
Red Sea Coast 30 61 121 182 243 303 364 425
Total 598 203 405 810 1,215 1,620 2,025 2,430 2,835

The total runoff was estimated using the rainfall intensities in different months, their corresponding areas and runoff coefficients (0.05–0.70). Generation of runoff in the SW region was estimated to be in the range of 203–2,835 MCM per year. In Case I, annual runoff was estimated to be 88, 53, 32 and 30 MCM in Asir, Jazan, Al-Baha and Red Sea Coast, respectively. For an intermediate scenario, for example, Case IV, runoff was estimated to be 527, 316, 190 and 182 MCM in these areas, respectively. For Case VIII (maximum), the runoff was predicted as 1,230, 738, 443 and 425 MCM, respectively. However, the storage capacities of the existing dams in Asir, Jazan and Al-Baha are 373, 194 and 31 MCM, respectively. No storage dam was reported in the Red Sea Coast. The data indicate that in Case I, 0.4 and 30 MCM per year of runoff are not collected in Al-Baha and the Red Sea Coast, respectively. In Case IV, approximately 154, 122, 159 and 182 MCM per year of runoff are not collected in Asir, Jazan, Al-Baha and the Red Sea Coast, respectively, while in Case VIII, 857, 544, 411 and 425 MCM per year of runoff are not collected in these areas, respectively. While comparing with Case I, approximately 85% of the annual runoff in the SW region is collected, in which the runoff in the Red Sea Coast is not collected at all. In Case IV, 49.2% of runoff in the SW region is collected. Asir, Jazan and Al-Baha collect approximately 70.8, 61.3 and 16.3% of the annual runoff, respectively. In Case VIII, approximately 30.3, 26.3, 7.0% of runoff is collected in Asir, Jazan and Al-Baha, respectively. Further details on the runoff loss can be found in Table 8.

Table 8

Runoff wastage in the south-western region of Saudi Arabia (MCM/year)

Runoff wastagea

Area Case I Case II Case III Case IV Case V Case VI Case VII Case VIII
Asir – – – 154 330 505 681 857
Jazan – – 17 122 228 333 439 544
Baha 0.4 32 95 159 222 285 348 411
Red Sea Coast 30 61 121 182 243 303 364 425
Total 31 93 233 617 1,023 1,426 1,832 2,237
Runoff wastagea

Area Case I Case II Case III Case IV Case V Case VI Case VII Case VIII
Asir – – – 154 330 505 681 857
Jazan – – 17 122 228 333 439 544
Baha 0.4 32 95 159 222 285 348 411
Red Sea Coast 30 61 121 182 243 303 364 425
Total 31 93 233 617 1,023 1,426 1,832 2,237

aCases I–VIII: C = 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, respectively.

The eight scenarios of runoff show that the uncollected runoff was in the range of 30.4–2,237 MCM/year (Tables 7 and 8), representing 15.0–78.9% of the total runoff. Figure 8 presents the dam capacities and predicted surface runoff for each area separately and in combination. The results show that the value of runoff coefficients need to be approximately 0.2 or more to exceed the current levels of storage capacities in Asir and Jazan (Table 8; Figure 8), while for Al-Baha and Red Sea Coast, even lower coefficients might lead to the loss of runoff. It should be noted that Şen & Al-Suba (2002) reported the runoff coefficients of 0.05, 0.07 and 0.07 for Baysh, Damad and Jazan wadies (SW region), respectively. However, it is likely that the runoff coefficients for the mountains will be higher than the runoff coefficients in the wadies (Holko & Kostka 2008). In Case I (Table 7), total runoff generations were estimated to be 203 MCM/year, which is much lower than the current storage of surface runoff (e.g., 598 MCM/year). However, runoff will still be lost, as there is no dam in the Red Sea Coast. Further, the floods in 2009, 2011 and 2013 indicated that the generations of surface runoff in these regions could be much higher than the dam capacities, meaning that the average runoff coefficients in these areas might be higher than Case I. Future study on runoff coefficients might better estimate the runoff in these areas.

Figure 8

Comparison of dams' capacity and runoff.

Figure 8

Comparison of dams' capacity and runoff.

## DISCUSSION

### Technical issues

The above assessment approximated the possible scenarios of runoff from the long-term rainfall patterns in the SW region of the country through considering a wide range of runoff coefficients. Several other limiting factors need to be considered to obtain better assessments, such as evaporation and permeability of water throughout the flow routes (e.g., wadies), distance from the rainfall stations to the dam locations, loads of solids with runoff, etc. Past studies have reported that the free surface evaporation from the wadies can be in the range of 5–80% of the water on an annual basis (Al-Turbak 1989; Al Maktoumi 2013; Lopez et al. 2014). Missimer et al. (2014) reported that up to 80% of the water in the old wadies could be lost through free surface evaporation. For a dam reservoir in the SW region of the country, the potential loss through surface evaporation was estimated to be in the range of 4.7–6 m per year (Lopez et al. 2014). The distance of the wadies that needs to be traveled by the runoff to reach the dam/reservoir can be another important factor. Significant amount of runoff can be lost through evaporation and infiltration while traveling to the dam/reservoirs. In addition, large amounts of solids can be accumulated in the dam/reservoirs during the flood events, which might reduce sub-surface water recharge significantly. Consequently, reduced recharge of water is expected in the aquifer (Missimer et al. 2014). The feasibility of dam construction and maintenance costs are the other factors to be taken into consideration. Construction of Wadi dams is quite expensive with costs ranging from $250 million to over$1 billion USD depending on the size and complexity of the dam (Missimer et al. 2014). In addition, water transportation from these sources and maintenance costs for the pipelines can also be significant. The complexity indicates that actions will be needed to minimize the effects of evaporation in the dam. In addition, the effects of solid deposits on water recharge need to be minimized. One of the possibilities may include water recharge through considering several small zones for water ponding and constructions of shallow wells in these zones. However, well construction, maintenance, porosity of the mediums under the wells, cost of pressurized recharge and solid depositions can be limiting factors for this option. It is advisable to perform optimization studies through incorporating the related factors for maximizing the benefits from rainfall in the SW region.

### Policy implications

Studies have demonstrated that Saudi Arabia needs water conservation, TWW reuse for agriculture, and to find new sources of water (MOEP 2010; Chowdhury & Al-Zahrani 2013a, b). The desalination plants supplied approximately 1,050 MCM of DW in 2009 (MOEP 2010; SWCC 2011), which increased to 1,595 MCM in 2013 (MOWE 2013). The MOEP had a plan to increase the desalination plants from 30 to 44 by 2014, which were projected to produce 2,070 MCM of DW in 2014 (MOEP 2010). In 2014, the predicted domestic water demand was 2,583 MCM, indicating the needs of additional water from other sources (MOEP 2010; Chowdhury & Al-Zahrani 2013a). The MOEP indicated that agricultural water demand would be decreased from 15,464 to 12,794 MCM from 2009 to 2014 (MOEP 2010). During this period, the industrial water demand was predicted to increase from 713 to 930 MCM. The MOWE reported that 15,408 and 14,999 MCM of GW was supplied to different regions in 2011 and 2012, respectively (MOWE 2013). In addition, 449 dams with a capacity of 2.02 BCM were used for recharge, flood control, and to supply water for domestic and irrigation purposes in 2012 (MOWE 2013). In 2012, a total of 81 wastewater treatment plants treated approximately 1,261 MCM of domestic wastewater while only 181 MCM of TWW was reused (MOWE 2013). However, the MOEP data showed that the reuse of TWW was 325 MCM in 2009 (MOEP 2010). The MOWE and MOEP data indicate that a significant amount of wastewater and TWW was not reused.

Past studies have reported that construction of infrastructure to collect and treat domestic wastewater and to recycle TWW for agriculture might provide significant support toward conserving NGW (Chowdhury & Al-Zahrani 2013b, c). These studies have demonstrated that comprehensive reuse of TWW might produce approximately 654 thousand tons of wheat, which was about 20% of the national wheat demand in 2011. The country had a plan to increase TWW reuse from 325 to 570 MCM by 2014 (MOEP 2010), which is still much less than the generated domestic wastewater (Chowdhury & Al-Zahrani 2013b, c). An aggressive policy to increase TWW reuse may be beneficial to the country, while comprehensive reuse of TWW requires significant costs and maintenance, which deserves the attention of the policy-makers.

In addition to the support from TWW reuse, new sources of water are required. The option of importing water from neighboring countries requires long-term political stability, cost and bi-lateral relationships. Although transferring water from one region to another region has been practised in some countries (e.g., Libya and China), Saudi Arabia lacks such sources (Mays 2011). Finding new sources within the country might be a better option (Chowdhury & Al-Zahrani 2013a). Harvesting runoff might be an emerging option in Saudi Arabia. Although the countrywide average annual rainfall is low, this study shows that significant fractions of runoff are being wasted from the SW region. By varying the runoff coefficients from 0.05 to 0.7, this study estimated much higher runoff generations than the capacities of the existing dams (Tables 7 and 8). The flash floods from the torrential rain in the SW region indicated higher runoff from rainfall events and/or poor drainage facilities (BBC News 2009; CNN World 2011; Arab News 2013). Through constructing new dams in the appropriate locations of the SW region, the country may increase runoff collection by 30.4–2,237 MCM/year. Such collection can lower NGW extraction, which is a strategic priority of the country. A policy to look into the possibility of increasing runoff collection from the SW region can help in water resources management, while such policy can also reduce dependency on the NGW sources. However, construction of large dams requires comprehensive study on the locations, elevations, IDF curves, rainfall–runoff relationship, flow directions, runoff coefficients and economic viability. In addition, higher rates of surface evaporation and accumulation of solids at the bottom of the dam reservoirs need careful attention. This indicates that faster rates of recharge may be an option, while the faster rates can be obtained through constructing shallow wells at the appropriate locations. Alternatively, storing water in underground tank/reservoirs might be another option. Future study is warranted to address these points.

## SUMMARY AND CONCLUSIONS

In Saudi Arabia, fossil water is limited and non-renewable in terms of real-time recharge at a particular hotspot. There might be an opportunity to increase runoff collection by constructing new dams/wells in the SW region. By analysing the rainfall, this study shows the potentials for additional runoff collection in the SW region. The total runoff generations in eight scenarios can be in the range of 203–2,835 MCM per year. In any scenario, loss of runoff is likely (Table 8). Availability of infrastructure (dam, well, etc.) may provide significant support for water resources management. For example, at runoff coefficient of 0.05, Asir, Jazan, Al-Baha and the Coast have the potential to collect approximately 0.0, 0.0, 0.4 and 30 MCM/year of additional runoff, which can be increased to 154, 122, 159 and 182 MCM/year at runoff coefficient of 0.3 (Case IV). At higher runoff coefficients, these values are likely to be higher. In the context of agriculture, 30.4 MCM/year of water (e.g., additional runoff for Case I) may produce approximately 12.2 thousand tons of wheat annually (at the rate of 2,492 m3/ton). For Case IV, this can be 249 thousand tons, which is approximately 7.5% of the national wheat demand in 2011.

The contour maps assist in identifying the approximate locations of new dams and/or wells for water storage and/or recharge. However, to identify the exact locations for new dams or wells, further details are needed on the locations, IDF curves, evaporation, water flow directions, water seepage and structural and geological feasibility. Future study should focus in these directions. In addition, runoff estimates can be improved by using the IDF. Future study should try to develop the IDF curves for these areas. This paper represents the first phase of the study to shed light on the importance and potentials for collecting surface runoff from the SW region of Saudi Arabia.

## ACKNOWLEDGEMENTS

The author(s) would like to acknowledge the support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM) for funding this work through project No. RG 1302-1 & 2.

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