Introduction

Flash flooding is a rapid and extreme effect of rainfall in a very short period (Hoedjes et al. 2014; Starosolszky and Melder 2014; Archer and Fowler 2015; Deng et al. 2015). The enormous amounts of rainwater can be exploited for different applications such as rainwater harvesting, recharging artificial reservoirs, irrigation, and reuse to supply drinking water (Angelakis 2016; GhaffarianHoseini et al. 2016). However, such massive amounts of water are also catastrophic and can cause destruction (Abbas et al. 2016; Dale et al. 2016; Karagiorgos et al. 2016). Rainfall water becomes a threat when flood control systems are unable to accommodate the enormous volumes of water during storms. Therefore, the massive amount of water may threaten regions, such as agricultural, industrial, and urban areas (Elfeki et al. 2017). Calculating the runoff volume is useful for mitigating flood risk and exploiting huge amounts of rainfall water (Masseroni et al. 2016). Many methods have recently been introduced to estimate the amount of runoff water, such as the peak discharge method, tabular method, unit hydrograph method, constant loss rate method, and initial loss-constant loss rate method (Moon et al. 2016; Nonglait and Tiwari 2016; Mistry et al. 2017). One widely used method to calculate runoff is the natural resources conservation service (NRCS) method, which was previously known as the soil conservation service (SCS) method (Pitt 1999; Patil et al. 2008; Ebrahimian et al. 2009; Bhagat 2016; Shah and Bhagat 2017). The NRCS method for estimating the runoff curve number (CN) was developed by the United States Department of Agriculture (USDA) (Cronshey 1986). This method depends on precipitation, potential maximum retention after runoff begins, and initial abstraction (Hong et al. 2007; Ebrahimian 2012; Ajmal et al. 2016; Ryu et al. 2016; Abdullah et al. 2017; Singh et al. 2017). The potential maximum retention after runoff begins is related to the CN (Durán-Barroso et al. 2016; Lal et al. 2016). Hence, the NRCS method relies mainly on precipitation and the CN.

A particular CN for an area is associated with data of hydrologic soil group (HSG), land use/land cover (LULC), treatment, hydrologic condition, antecedent runoff condition (ARC), and integrated pervious and impervious areas (Mishra and Singh 2013; Ryu et al. 2016; Mahmoud and Gan 2018d). The HSG is very essential for categorizing different soils into specific groups according to their infiltration rates (NRCS 2007), which are similar in terms of physical and runoff characteristics. Factors affecting the HSG are saturated hydraulic conductivity of the layer of least transmissivity, depth to the water impermeable layer, and depth to the high water table. Of these, the most influential factor is hydraulic conductivity (Lee et al. 2016). According to NRCS, the HSG was initially classified into four groups, namely A, B, C, and D, and recently, three new dual groups of A/D, B/D, and C/D were added (NRCS 2009). In the four single groups, “A” refers to soils with high infiltration rates and low potential runoff; “D” represents soils with a low infiltration rate and high potential runoff; and “B” and “C” indicate moderate and slow infiltration rates, respectively (Shadeed and Almasri 2010; Ahmad et al. 2015).

The LULC data provides useful information for describing the land use and land cover types of a particular area. The extent of LULC covers several categories such as water bodies, agricultural land, built-up land, barren land, and roads (Fisher et al. 2005). The classification process of these categories is extensive and intensive work. Thus, the process of developing LULC datasets generally depends on satellite images (Mack et al. 2017; Zhang et al. 2017). The LULC developed through satellite images can distinguish land features into four classes, namely urban, barren land, agricultural land, and roads. Each of these has a unique CN value according to the infiltration rate. The CN value ranges from 0 to 100, which refers to low and high runoff extremes, respectively (Li et al. 2015). In general, land use change influencing local temperature and precipitation (Mahmoud and Gan 2018a; Mahmoud and Gan 2018b). The treatment describes the cultivation method used in agricultural lands including tillage, hoeing, sowing, contouring, and terracing (Cronshey 1986). Meanwhile, the hydrologic condition expresses runoff or infiltration under the treatment and cover type (Gajbhiye et al. 2014). The three cases of the hydrologic condition (good, fair, and poor) are given in descending order with respect to the infiltration rate (Cronshey 1986). Generally, a good hydrologic condition has high infiltration and low runoff. On the contrary, a poor hydrologic condition has low infiltration and high runoff. The ARC, or pre-storm soil moisture, is considered one important factor affecting the CN and is defined as the runoff potential index before the occurrence of storm events. There are three cases of ARC according to NRCS: I, II, and III (Cronshey 1986). The values of these cases are arranged in descending order with respect to soil moisture (Oliveira et al. 2016). Case (I) has dry soil but not to the wilting point, while in contrast, the case (III) has saturated soil as a result of heavy or light rainfall for the last 5 days. In general, the NRCS adopts the average case, II, to estimate CN values (Sartori et al. 2011), although the CN values should also be adjusted for the other two cases to avoid sudden jumps in runoff estimation. Furthermore, the CN value varies in the cases of connected or unconnected impervious areas. If the impervious areas are directly connected to the drainage system, water loss by infiltration does not occur (Cronshey 1986).

The potential runoff (Q) for every cell can be determined by the CN equation (\( \mathrm{Q}=\frac{\ {\left(\mathrm{P}-{\mathrm{I}}_{\mathrm{a}}\right)}^2}{\left(\mathrm{P}-{\mathrm{I}}_{\mathrm{a}}\right)+\mathrm{S}} \)) (Salih and Hamid 2017; Singh et al. 2017). From this equation, three factors influencing runoff are identified in units of millimeters (Anaba et al. 2017; Wang et al. 2017): (1) P—precipitation, (2) S—potential maximum retention after runoff begins, and (3) Ia—initial abstraction. Furthermore, an existent relationship is present between S (a function of CN) and Ia. The initial abstraction plays an essential role in prognosticating the potential runoff. According to NRCS (2007), the initial abstraction ratio (λ) is 0.2. Because this value is ambiguous, several researchers have conducted experiments in attempts to validate it. For example, some of these studies found that the ratio varies from 0.01 to 0.154, with an average value of 0.048 (Shi et al. 2009; Yuan et al. 2014). Thus, the more realistic ratio is 0.05 (Woodward et al. 2003; Beck et al. 2009; Ajmal and Kim 2014). A proper determination of CN and λ values is definitely reflected in obtaining the optimum potential maximum retention and then reflected in the estimation of potential direct runoff. Therefore, this study used the Sobhani formula (Sobhani 1976) to convert normal CN (CNII) to the dry CN case (CNI), moreover, the Hawkins formula (Hawkins et al. 1985) to convert normal CN (CNII) to the wet CN case (CNIII).

Determining the Q through integrating geographic information systems (GIS) and remote sensing technique (RST) is a powerful technique that saves time and effort. As well as, the availability of precipitation data used in this technique which can be downloaded from the Climate Forecast System Reanalysis (CFSR) of the National Centers for Environmental Prediction (NCEP) (Dile and Srinivasan 2014; Fuka et al. 2014; Rajeevan 2017; Tirkey et al. 2017). Several studies have applied this integration to estimate potential runoff (Chavda et al. 2016; Harish et al. 2016; Jaber et al. 2016; Patel and Trivedi 2016). The GIS data in such studies have been used in watershed delineation, geo-referencing, digitizing, map projection, CN distribution, and runoff estimation. Meanwhile, RST has been utilized in classifying satellite images for LULC. Recently, the Riyadh metropolitan area, Saudi Arabia, experienced flash flooding that resulted in damages such as socioeconomic loss, soil erosion, land degradation, and vegetation loss in addition to the inundation of cities, destruction of infrastructure, and loss of lives (Khan 2011; Mahmood and Mayo 2016; Mahmood and Ullah 2016; Ranjan 2017).

Therefore, this study aims to estimate the CN and potential direct runoff volume for urban watersheds of the Riyadh metropolitan area based on integrated GIS and RST data. Moreover, it provides a good regional case study for future assistance to the decision-makers in mitigating the flood risk, rainwater harvesting, and rainfall-runoff assessment.

Site descriptions

The study area is the urban city of Riyadh in the Kingdom of Saudi Arabia (KSA), located between latitude 24°13′51′′ N to 25°10′30′′ N and longitude 45°59′12′′ E to 47°20′29′′ E (Fig. 1). The area of the city is 6570 km2 (including 1800 km2 of urbanized area), while the watershed area measures about 8500 km2. This urban area is characterized by horizontal expansion with vast infrastructure and agricultural and industrial areas (Rahman et al. 2016; Sharif et al. 2016). Additionally, demographically, Riyadh is one of the fastest growing cities with a high population intensity of 6.5 million people (Ashwan et al. 2012; Mahmoud and Gan 2019). The climate of Riyadh City is an extremely hot desert with sweltering temperatures during summer and a warm cool climate in winter. Despite a meager annual precipitation rate (Mahmoud and Gan 2018c) of about 62 mm, the city periodically experiences heavy rainfall events that lead to flash flooding.

Fig. 1
figure 1

Location map of Riyadh metropolitan area

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Materials and methods

The potential runoff in the present is one of the most important factors of flood risk mitigation and rainfall water harvesting. It is estimated according to the NRCS-CN method. Mainly, this method is used to calculate the CN as a function of LULC and HSG for the study area. Figure 2 illustrates the applied methodology for CN estimation and mapping, which employed DEM, soil map, geology map, and satellite image data as well as daily precipitation records (Table 1). The applied projection of this study is the WGS 84 UTM zone 38 coordinate system. Three steps have been used to calculate the CN based on available data as follows:

Fig. 2
figure 2

Applied GIS-based methodology for the estimation curve number (CN) of the study area

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Table 1 Data used in the study and sources (The year of use for all data is 2017)
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Firstly, DEM data of the United States Geological Survey (USGS) with a 30-m resolution (Fig. 3) was used to delineate the watersheds of the Riyadh metropolitan area with the aid of ArcGIS 10.4 platform. Besides, slope, aspect, hillshade, and contour maps were created, as shown in Figs. 4, 5, 6, and 7, respectively.

Fig. 3
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Digital elevation model (DEM) of the study area

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Fig. 4
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Slope map of the study area

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Fig. 5
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Aspect map of the study area

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Fig. 6
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Hillshade map of the study area

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Fig. 7
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Contour map of the study area

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Secondly, the HSG was developed for the study area by using a soil map (Fig. 8) and geologic map (Fig. 9) obtained from the Saudi Ministry of Environment, Water and Agriculture (MEWA) and the Saudi Geology Survey (SGS), respectively. Both maps were downloaded as joint photographic experts group (JPEG) images, which require geo-referencing, digitizing, reclassifying, and clipping. The soil map codes and their hydraulic conductivity data are listed in Table 2. The combination of these two maps resulted in the HSG classification.

Fig. 8
figure 8

Soil map of the study area

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Fig. 9
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Geology map of the study area

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Table 2 Soil map codes with corresponding hydraulic conductivity (cm/h), water impermeable layer (cm), and soil texture at a water table depth of more than 150 cm (data available at http://gis.moa.gov.sa/gp/en/Default.aspx)
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Finally, the LULC was created for the study area by using a Landsat 8 image with 30 m resolution (Fig. 1). This image was retrieved from USGS and manipulated as unsupervised and supervised classifications by employing ENVI 5.3 software. The supervised map of the study area was classified into four land features: urban, barren land, agricultural land, and roads. The supervised classification of LULC is adopted for this study because it is more distinguishable than the unsupervised classification.

Estimation of the CN for every cell of the study area was performed using the combination tool incorporated in ArcGIS 10.4. Accordingly, the CN map was generated by combining HSG and LULC maps under ARC II conditions (Table 3). The weighted area method was adopted to determine the weighted CN of each watershed in the study area, which was achieved by multiplying the value of the watershed CN by its area. Therefore, the following equations were used in developing the weighted CN map for each watershed.

$$ \mathrm{Q}=\frac{\ {\left(\mathrm{P}-{\mathrm{I}}_{\mathrm{a}}\right)}^2}{\left(\mathrm{P}-{\mathrm{I}}_{\mathrm{a}}\right)+\mathrm{S}} $$
(1)
$$ {\mathrm{I}}_{\mathrm{a}}=0.05\mathrm{S} $$
(2)
$$ \mathrm{S}=\frac{25400}{\mathrm{CN}}-254 $$
(3)
$$ {\mathrm{CN}}_{\mathrm{w}}=\frac{\sum {\mathrm{A}}_{\mathrm{i}}{\mathrm{CN}}_{\mathrm{i}}}{\sum {\mathrm{A}}_{\mathrm{i}}} $$
(4)
Table 3 Curve number (CN) values for land use/land cover (LULC) and hydrologic soil group (HSG) under all antecedent runoff conditions (ARC): I, II, III conditions
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Where CNw is the weighted CN used for runoff volume computations; CNi the CN of sub-area i; and Ai the area of sub-area i.

The CN values were adjusted for dry (I) and wet (III) ARC cases to avoid the unexpected jumps during the runoff estimation. Mishra et al. (2008) reported that the Sobhani formula (Sobhani 1976) and Hawkins formula (Hawkins et al. 1985) are the best conversion method for CNI (Eq. 5) and CNIII (Eq. 6), respectively.

$$ {\mathrm{CN}}_{\mathrm{I}}=\frac{{\mathrm{CN}}_{\mathrm{I}\mathrm{I}}}{2.334-0.01334{\mathrm{CN}}_{\mathrm{I}\mathrm{I}}} $$
(5)
$$ {\mathrm{CN}}_{\mathrm{II}\mathrm{I}}=\frac{{\mathrm{CN}}_{\mathrm{II}}}{0.427+0.00573{\mathrm{CN}}_{\mathrm{II}}} $$
(6)

The potential runoff (Q) for every cell was then estimated by (1) determining the potential maximum retention after runoff begins (S) based on the CN value for each pixel, (2) calculating the initial abstraction (Ia), and (3) estimating the potential direct runoff according to the maximum daily rainfall data of CFSR (Fig. 10).

Fig. 10
figure 10

Maximum daily precipitation distribution map of the study area

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Results and discussion

The NRCS-CN method is widely used because of its ease of application and adaptability to small territories. According to the DEM, 40 watersheds with a total area of 8500 km2 were delineated in the Riyadh metropolitan area as shown in Fig. 11. Table 4 describes each watershed and its characteristic factors, as well as its corresponding CN and Q in millimeters. Watersheds 9, 12, 14, and 17 encompass more than 80% of the entire study area. Regarding the average slope of the watershed, only three watersheds, namely 31, 33, and 34, have an average terrain slope of more than 15% with an average maximum slope of 17.3, 16.5, and 16.2%, respectively. In addition, 35 watersheds have slopes less than 10%. Among these watersheds, the lowest slope of which are 18, 19, and 21 by an average slope of 2.7, 2.5, and 2.6%, respectively.

Fig. 11
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Delineated watersheds of the study area

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Table 4 Curve number (CN) of watersheds with hydrologic soil group (HSG)
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Figure 12 depicts the HSG of the study area, which is characterized by four groups: A, B, C, and D. The HSG of D (clay loam) is the common obvious group, comprising about 71% of the total study area. This means that most of the area has high potential runoff and low infiltration rates whereby water is transmitted finitely through the soil. These conditions indicate the presence of impervious materials therein. Group B (loam) follows in terms of coverage (26%). Whereas, groups A (sand) and C (sandy clay loam) do not exceed 5%. Therefore, the area is at risk of experiencing runoff during storm events.

Fig. 12
figure 12

Hydrologic soil group (HSG) map of the study area

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Land cover is recognized as an essential parameter, affecting Q and flood behavior. In this study, both unsupervised and supervised classifications were used. Figure 13 shows the unsupervised land cover classes. Although this map has six classes (1 to 6), some land features such as the road layer do not appear. Thus, an unsupervised classification cannot adequately distinguish land cover types. Conversely, the supervised map can differentiate more details in the land cover. Figure 14 shows the supervised land cover of the study area, which consists of four land cover classes, namely urban, barren land, agricultural land, and roads. The majority of the study area is barren land, which covers 87.85% of the total area, while the land cover of urban areas, agricultural lands, and roads are 9, 1.5, and 1.65%, respectively. Moreover, barren land is on the outskirts of the study area, whereas the remaining land cover classes are concentrated in the center.

Fig. 13
figure 13

Unsupervised land cover map of the study area

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Fig. 14
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Supervised land cover map of the study area

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The CN values distributed in the study area for every cell from 64 to 98 are shown in Fig. 15. These CN values were used to calculate the weighted CN for every watershed (Fig. 16). Figures 15 and 16 confirm that about 80% of the watersheds have CN values higher than 90. The highest CN values cover barren, urban land, and roads, while the moderate CN values cover the agricultural land. These results indicate that the underlying lithology in the study area has high impermeability in most places and a low amount of vegetation cover, leading to a high runoff and a very low infiltration rate. Therefore, the weighted CN of the study area is 92, which also emphasizes the previous result. The slope map illustrates that the slope is classified into five classes: very low (< 2.5), low (2.5–6.5), medium (> 6.5–12.5), high (> 12.5–20.5), and very high (> 20.5) degrees, where the slope varies from 0° to 52°. Hence, the study area slopes south to southeast, which is clearly indicated in the slope direction and hillshade maps. This evidence confirms the aforementioned nature of runoff and infiltration.

Fig. 15
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Curve number (CN) map for every cell of the study area

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Fig. 16
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Weighed curve number (CN) map of the study area watersheds

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The maximum daily precipitation ranges from 42 to 63 mm from center to southwest of the city. Figure 17 classifies the potential maximum retention (S) into five classes: very low (< 19), low (19–31), medium (> 31–41), high (> 41–61), and very high (> 61) mm. Noteworthy is that the very low class covers most of the study area and is widespread in the west and northwest, because the highest daily potential runoff depth is located in the same regions of the study area (Fig. 18). The runoff depth is also classified into five classes: very low (< 15), low (15–25), medium (> 25–35), high (> 35–50), and very high (> 50) mm. Therefore, monthly and annual runoff can be derived from the maximum daily runoff. The very low and low potential runoffs are restricted in the study area, whereas the medium potential runoff has a low to moderate influence. High and very high runoffs threaten most places in the Riyadh metropolitan area, which can lead to catastrophic damages to property and harm to lives.

Fig. 17
figure 17

Potential maximum retention (S) map of the study area

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Fig. 18
figure 18

Potential runoff (Q) map of the study area

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Conclusions

Flash flooding, a rapid and extreme effect of rainfall, is considered the worst flood type, because of the unexpected and devastating results thereof. Therefore, identifying the areas that may be at risk of flash flooding is crucial to help mitigate efforts. Hence, the NRCS-CN method and GIS were integrated to estimate the potential runoff for the Riyadh metropolitan area to augment output accuracy. The results show that the values of CN, precipitation, and runoff depth are 64–98, 42–63, and 10 to 59 mm, respectively.

Furthermore, 133 districts in the study area were shown to have very high potential runoff while only 8 districts demonstrated high potential runoff. This work was based on the integration of GIS and RST. The results can be used as an effective tool to help decision-makers in planning and managing watersheds for conducting more related studies in the area.