Abstract

Flood risk assessment in ungauged watersheds remains a challenge due to limited flow data. This study investigates peak discharge and flood risk in the ungauged Wupa River Basin, Nigeria, using Manning's equation, the Kinematic Wave Parameter (KWP) model, and the Natural Resources Conservation Service – Curve Number (NRCS-CN) method. The thorough analysis provides valuable insights into peak discharge dynamics, underscoring the significance of accurate hydrological modeling and watershed characterization. Results indicate that Manning's equation and KWP produce similar peak discharge estimates (e.g., 155.71 m³/s and 155.98 m³/s for September 2022), whereas the NRCS-CN method yields significantly higher values (376.80 m³/s for the same month) due to its sensitivity to soil and land use characteristics. The study also addresses the potential inadequacy of the NRCS-CN method for forested areas in West Africa. These findings provide critical insights for flood management and infrastructure planning in ungauged basins across West Africa.

1 Introduction

Flooding emerges as a predominant natural calamity in Nigeria, with a rising number of states grappling with recurrent inundations during the rainy seasons, attributed to heightened precipitation patterns linked to climate variability (Echendu 2020). Yet, distinct from certain other natural catastrophes, flood-related disasters stemming from torrential rainfall are amenable to mitigation through meticulous planning and strategic interventions (Echendu 2023). The prevalent incidence of flood disasters in Nigeria predominantly stems from deficiencies in urban planning methodologies or insufficiently robust infrastructure frameworks (Oladokun and Proverbs 2016).

In ungauged basins, indirect peak discharge estimation methods are commonly used to assess flood risks (Smith et al. 2018). However, the reliability of these methods varies depending on catchment characteristics, rainfall patterns, and land-use changes (Kästner et al. 2018). This study addresses the critical gap in hydrological modeling for ungauged basins by evaluating the performance of Manning’s equation, KWP, and NRCS-CN methods in estimating peak discharge for the Wupa River Basin in Nigeria.

This study aims to evaluate and compare the performance of these three methods within the ungauged Wupa River Basin in Abuja, Nigeria, where the rainy season typically spans from April through late October, occasionally extending into November (Stein et al. 2020). During this period, heavy rainfall can rapidly elevate streamflow to peak discharge levels within minutes to hours, often resulting in severe flooding, particularly between June and September. This seasonal pattern aligns with documented trends of increased precipitation during these months, as illustrated in Figure 1 (World Bank 2024).

Figure 1 Distribution of temperature and mean annual rainfall (1991–2020) in Nigeria.

Most existing studies on flood risk assessment in Nigeria have focused on large river systems with available hydrological records, neglecting smaller urban catchments that experience severe flooding (Umar and Gray 2023). Moreover, there is limited comparative analysis of different peak discharge estimation methods in data-scarce environments. Without a proper evaluation of these methods, flood management strategies in ungauged basins may be based on inaccurate predictions, leading to ineffective mitigation efforts (Okacha et al. 2024).

This research is one of the first comprehensive comparative studies evaluating multiple indirect flood estimation methods in an ungauged river basin in the region. While several studies have applied these methods separately (Aladejana 2021; Ezemonye et al. 2016; Idowu et al. 2025; Isagba et al. 2021), their comparative performance in the context of urban hydrology in Nigeria remains unexamined. By providing a detailed evaluation, this study offers insights that can enhance flood risk assessment, urban planning, and climate adaptation strategies in developing regions with similar hydrological challenges.

Furthermore, the findings will serve as a benchmark for policymakers, engineers, and disaster management authorities in selecting appropriate flood estimation techniques for ungauged basins. The study also contributes to the broader field of hydrology by examining the applicability of these models under conditions of limited hydrological data.

2 Materials and Methods

The study area encompasses the Wupa River, situated within the Federal Capital Territory (FCT) region of Nigeria. Originating within the city limits of Abuja, the Wupa River traverses approximately 100 km. Exiting Abuja, it meanders through numerous villages and settlements before joining with the Gurara River. Ultimately, it merges into the Niger River, which holds the distinction of being the longest river in West Africa and the third-longest on the continent (Lamine et al. 2021). Figure 2 depicts the delineated watershed for the analysis point along the Wupa River, with an area of 192 km² and an average altitude of approximately 267 meters above sea level (masl). Upstream, the altitude reaches approximately 482 m (9° 01' 40.55'' N; 7° 29' 23.27'' E), while downstream, it descends to about 114 m (8° 53' 44.30'' N; 6° 53' 18.64'' E).

Figure 2 Map of the Wupa River, Nigeria.

The Wupa River’s primary water inputs are from two main sources: surface runoff generated by rainfall and seepage from groundwater. Consequently, Figure 3 illustrates a notable fluctuation in water levels between the rainy season and the harmattan season. Furthermore, the Wupa Treatment Plant plays a significant role in influencing the river's water composition. Designed with a capacity to treat up to 131,250 m³ of wastewater per day, the plant serves as a crucial facility for purifying the majority of Abuja's wastewater. As a result, the treated effluent from the Wupa Treatment Plant is discharged into the Wupa River, further impacting its water quality (Balogun and Ogwueleka 2021; Ibangha et al. 2024).

Figure 3 Wupa River during the harmattan (left), and the rainy season (right) from the Nile University of Nigeria campus.

Abuja, located within the tropics and classified under the Köppen climate system (Koko et al. 2021), exhibits a tropical wet and dry climate, characterized by three distinct weather conditions annually. The year begins with the harmattan season (November–January/ February), driven by the northeast trade wind and marked by dust haze and drought. This is followed by a brief dry season (typically February–March), after which the warm, humid rainy season sets in and persists from April to October. The topography of the FCT, characterized by high elevations and undulating terrain, exerts a significant influence on the region's weather patterns (Igbokwe et al. 2024).

2.1 Method

As illustrated in Figure 4, the research methodology followed a systematic approach comprising three main components: literature review, field investigation, and discharge estimation. The literature review phase involved comprehensive analysis of books and articles, leading to the identification and selection of appropriate hydrological models.

Figure 4 Research methodology flowchart.

Field investigations were conducted to gather essential data, including channel geometry measurements, surface roughness assessments, slope and flow velocity validation, and land use and soil data collection. The discharge estimation phase employed three distinct methods: Manning’s equation, the KWP model, and the NRCS-CN method, each requiring specific parameters as detailed in the flowchart. Manning’s equation utilized five basic parameters, while the KWP model required six parameters, sharing some commonalities with Manning's equation. The NRCS-CN method proved the most parameter-intensive, requiring eight distinct inputs for comprehensive analysis.

2.2 Manning’s Equation and discharge estimation

In most studies, it is highlighted that Manning’s equation serves as a primary tool for calculating discharge in conventional open channels (Mir and Patel 2024; Salah Abd Elmoaty and El-Samman 2020). Manning's equation, an empirical formula, is tailored for uniform flow conditions in open channels and is contingent upon parameters such as flow area, channel velocity, and channel slope. This equation operates under the assumption of uniform flow, where the bed slope of the channel aligns parallel to both the energy grade line and the water surface slope (Bouabdellah 2022).

The hydraulic radius holds significant importance in both open channels and pipelines, playing a pivotal role in hydraulic calculations. Its determination relies on various mathematical equations, which differ based on the cross-sectional shape of the open channel, whether circular, rectangular, triangular, or trapezoidal. Figure 5 illustrates a trapezoidal open channel cross-section, with parameters essential for characterizing its size and shape (Vatankhah 2023). These parameters include b, representing the bottom width; w, denoting the wetted length along the sloped side; y, indicating the water depth; and θ, specifying the angle of the sloped edge relative to the horizontal plane.

Figure 5 Geometry of a trapezoidal channel segment.

As seen in Figure 6, like most natural channels, the cross-sectional area of the Wupa River is closer to the trapezoidal shape (Samarinas and Evangelides 2021; Wang et al. 2016) with equal side slopes.

Figure 6 Trapezoidal cross-section of the Wupa River (January 2022).

The hydraulic radius (R_h) is calculated as the ratio of the flow area (A) to the wetted perimeter (P) of the channel. While there isn't a universal solution for arbitrary cross-sections, focusing on the evaluation of the trapezoidal segment provides fundamental insights. Assuming a generalized symmetric trapezoid with an angle θ, the flow area can be computed using the following expressions in Equations 1 and 2:

(1)

The wetted perimeter is:

(2)

Where:

b	=	bottom width of the channel,
w	=	wetted length measured along the sloped side,
y	=	water depth,
θ	=	angle of the sloped edge from the horizontal plane,
cot θ	=	cotangent of the angle θ,
βy	=	product of cot θ and y,
A	=	flow area,
P	=	wetted perimeter, and
Rh	=	hydraulic radius.

The geometric parameters of the Wupa River channel were measured during the harmattan season (January) when water levels were at their lowest, allowing for safer and more accurate measurements. The b of 18.6 m was measured using a measuring tape at the water surface level. Channel depth (y) of 2.4 m was determined using a graduated surveying rod at multiple points across the channel cross-section, with the average value reported. The wetted length along the sloped side (w) of 4.17 m was measured using a measuring tape extended along the bank slope. The side slope angle (θ) of 37° was determined using a digital inclinometer at multiple points along both banks, with the average value used for calculations. All measurements were taken at three different cross-sections within a 50 m reach and averaged to account for local variations in channel geometry.

Table 1 presents the calculation of the hydraulic radius (R_h) of the Wupa River at a specific studied point:

Table 1 Calculation of hydraulic radius (R_h) of the Wupa River at a studied point.

Site	b (m)	w (m)	y (m)	θ	cot 37°	βy (m)	A (m2)	P (m)	Rh (m)
Wupa River within the area of Nile University of Nigeria	18.6	4.17	2.4	37°	1.33	3.19	52.28	26.94	1.94

Based on the provided dimensions and calculated values in Table 1, the calculations of the wetted area and wetted perimeter were performed using Equations 1 and 2, followed by the calculation of the hydraulic radius (R_h), which is the ratio of the cross-sectional area to the wetted perimeter yielding 1.94 m.

The mean velocity of streamflow is influenced by several factors including the gradient, channel bed roughness, and the form of the cross-sectional area of the channel. Manning’s equation is commonly used to describe the mean velocity of flow (V₀, m/s), given by Equation 3:

(3)

Where:

n	=	Manning’s coefficient,
Rh	=	hydraulic radius (m), and
S0	=	channel slope (dimensionless).

In Manning’s equation, the Manning’s coefficient (n) is a crucial parameter that characterizes the roughness of the channel. This coefficient is influenced by several factors such as the size and type of materials forming the riverbed and channel sides, as well as the overall channel structure. Manning’s roughness coefficient is typically estimated from tables provided by references such as Singh and Chow (2017), or occasionally by visually comparing channel characteristics with images demonstrating identified roughness.

According to a report published by the US Geological Survey (Arcement and Schneider 1989), the Manning’s coefficient (n) can be calculated as follows.

(4)

Where:

nb	=	base value of n for a straight, uniform, smooth channel in natural materials,
n1	=	correction factor for the effect of surface irregularities,
n2	=	variations in shape and size of the channel cross-section,
n3	=	obstructions,
n4	=	vegetation and flow conditions, and
m	=	correction factor for meandering of the channel.

The ideal method for determining Manning's n would be through calibration using historical discharge and water level data. However, due to the ungauged nature of the Wupa River and lack of historical measurements, this study relied on published values. For the Wupa River, which is characterized by a relatively straight channel with a clean bed, full stage, and absence of cracks or gravel pools, yet with an abundance of rocks and vegetation, a Manning’s roughness coefficient (n = 0.035) was selected. This value, derived from the table suggested by Chow (Singh and Chow 2017) and supported by field observations of the river’s bed composition, reflects the specific roughness conditions of the channel and was applied in the implementation of Manning’s equation for flow velocity estimation.

2.3 Kinematic Wave Parameter (KWP) for flow velocity and discharge approximation

Kinematic Wave Models (KWM) find application in both channel and overland-flow routing within various hydrological modeling systems, including the Precipitation-Runoff Modeling system and the Distributed Routing Rainfall-Runoff Model (Bao et al. 2017). These models offer a simplified representation of the St. Venant equations, operating under the assumption that the riverbed slope closely approximates the friction slope. Due to its simplicity and accuracy, kinematic wave routing is commonly employed in modeling both open channel and overland flow (Vatankhah 2020).

The KWM is defined by Equations 5 and 6 (Park et al. 2021; Vatankhah 2020; Zheng et al. 2020). Equation 5 is the Continuity equation:

(5)

Equation 6 is the Momentum equation:

(6)

Where:

Q	=	discharge (m3/s), and
q	=	lateral inflow per unit length of channel (m2/s).

The parameters α and γ in Equation 6 are referred to as Kinematic Wave Parameters (KWP), and they are typically determined using Manning’s equation. Here, γ represents the dimensionless sensitivity of discharge to changes in flow area (i.e., the nonlinearity in the empirical relation Q = α·A^γ), while α is a dimensional scaling factor that reflects channel roughness, slope, and geometric characteristics. In the case of the Wupa River, where the channel edges resemble trapezoidal channels with similar side slopes (i.e., θ_R = θ_L), the following formula can be applied to estimate discharge through a trapezoidal channel, as suggested for KWP for trapezoidal channels with equal side slopes (Kumar 2020).

Equation 7 can be counted as the actual relationship between Q and A for a trapezoidal channel with equal side slopes.

(7)

Where:

QTE	=	discharge in a trapezoidal channel with equal side slopes, and
Ψ	=	dimensionless variable = A/b2.

2.4 NRCS-CN method for direct runoff estimation

The Natural Resources Conservation Service Curve Number (previously known as the Soil Conservation Service Curve Number) method was originally developed in 1954 and documented in Section 4 of the SCS National Engineering Handbook. This handbook was published by the Department of Agriculture of the U.S. Soil Conservation Service in 1956. Subsequent modifications to the handbook were made in 1964, 1965, 1971, 1972, 1985, and 1993, as noted by Meshram et al. (2017).

The NRCS-CN method typically involves five main steps:

1. Determination of watershed area (A): This step entails calculating the catchment area up to the point where measurements are taken. In this study, the watershed area was calculated using the Global Watersheds web application to be approximately 192 km².
2. Calculation of Curve Number (CN): The CN is determined based on the hydrological soil group of the river basin, which plays a crucial role at this stage. The CN values can be extracted from tables suggested by references such as Chow et al. (1988). For our study, soil classifications were derived from the 1990 Soil Map of Nigeria (seen in Figure 7) supplemented with satellite imagery to identify land use patterns.
3. Resolution of excess rainfall or event direct runoff (Q): This step involved using empirical relations derived from numerous experimental watersheds to calculate excess rainfall or Q, as described by Equation 8.
4. Calculation of time of concentration (T_c): T_c included the travel time for overland flow (T_t), shallow concentrated flow, and streamflow.
5. Computation of the hydrograph or peak runoff (q_p): Finally, the hydrograph or q_p in m³/s was computed using Equation 11.

These steps collectively form the process for estimating runoff using the NRCS-CN method, integrating various factors such as watershed characteristics, soil properties, and hydrological processes (Metselaar 2023) using Equation 8.

(8)

Where:

Qr	=	event direct runoff depth (mm),
P	=	event rainfall depth (mm),
S	=	storage index (mm), and
Ia	=	initial abstraction (mm).

The standard version of the curve number equation reduces the number of parameters to one by setting I_a to 0.2S (Ibrahim et al. 2022) in Equation 9:

(9)

The storage index (S) in mm can be estimated using Equation 10 (Eshghizadeh 2024):

(10)

Where:

CN (0 – 100)

=

so-called curve number which can be obtained from the land-use and hydrologic soil group tables provided in National Resources Conservation Service Technical Release No. 55 (TR-55) (Tables 2-2a to 2-2d) (Cronshey 1986).

The NRCS method employs Equation 11 to estimate peak discharge (Korenic 2022):

(11)

Where:

qp	=	peak discharge (m3/s),
qu	=	unit peak discharge in , also an empirical factor that depends on the time of concentration, rainfall, rainfall pattern, and initial losses,
A	=	drainage area (km2),
Qr	=	depth of runoff depth (mm), and
Fp	=	pond and swamp adjustment factor (accepted 0.87).

In many instances, the q_u may be ambiguously or inaccurately expressed. However, upon examining Equation 11, the unit provided above emerges as a clear and accurate representation, encompassing the rate of flow (m³/s), the area (km²), and the depth of runoff (mm).

The q_u value can be derived either from Exhibit 4-II (q_u for NRCS (SCS) type II rainfall distribution) in TR-55 or by utilizing Equation 12, provided below (Chin 2020).

(12)

Where:

Tc	=	time of concentration (hr) (minimum, 0.1; maximum, 10.0), and
C0, C1, C2	=	coefficients from Table F-1 located in Appendix F of TR‑55.

3 Results and discussion

3.1 Estimation of peak (full river flow) discharge using Manning’s equation

To initiate this calculation, the hydraulic radius has been computed based on a trapezoidal cross-section template (Figure 5), considering that the Wupa riverbed is observed to be either filled or flowing close to full after heavy rain. Utilizing the information provided in Table 1 and Manning’s equation (Equation 3), the flow rate of the filled Wupa River has been calculated and presented in Table 2. It can be inferred that the flow rate corresponding to the full bank capacity of a river equals the peak flow at a specific point along the river.

Table 2 Estimation of full bank discharge flow at study point by using Manning's equation.

Site	Hydraulic radius R (m)	Slope S (km/km)	Manning’s roughness coefficient, n	Manning’s equation V (m/s)	Cross-section area A (m2)	Discharge Q (m3/s)
Wupa River within the area of Nile University of Nigeria	2.05	0.0037	0.035	2.7	55.46	155.71

The average slope of the Wupa River has been determined by accounting for the variations in altitude relative to sea level between upstream and downstream points, as well as the length of the river. Subsequently, the velocity obtained from Manning's equation and the cross-sectional area of the Wupa River have been multiplied to calculate the full capacity volumetric flow, or peak discharge, which amounts to 151.71 m³/s.

3.2 Kinematic Wave Parameter (KWP) for flow velocity and discharge estimation

The application of the Kinematic Wave Parameter (KWP) model (Equation 7) on the Wupa River has been summarized in Table 3. The result of this calculation using the KWP method yielded a flow rate of 155.98 m³/s. Remarkably, this value is nearly identical to the result obtained using Manning’s method, further validating the accuracy and consistency of both approaches in estimating the peak discharge of the Wupa River.

Table 3 Required parameters for discharge calculation by Kinematic Wave Parameter.

Site	b (m)	Slope km/km (S)	Manning’s roughness coefficient (n)	cot 37°	Ψ (A/b2)	Cross-section area (A) (m2)	Discharge (QTE) (m3/s)
Wupa River within the area of Nile University of Nigeria	18.6	0.0037	0.035	1.327	0.16	55.46	155.98

3.3 NRCS-CN method and peak discharge

Based on the soil map of Nigeria (see Figure 7) it is observed that most of the catchment area comprises shallow and moderately deep to deep well-drained soils, along with somewhat poorly to poorly drained soils. The surface soils are predominantly categorized as loamy sand to sand loamy, occasionally with gravelly surfaces, overlaying sandy clay loam to sandy clay, sometimes with gravelly subsoils.

Figure 7 Soil map of Nigeria (ESDAC 1990).

Following the hydrologic soil group classification by the Natural Resources Conservation Service (NRCS 2022), these soil types are classified as belonging to Group A. This classification indicates that these soils exhibit high infiltration rates and low runoff potential, which is consistent with their characteristics of being well-drained and moderately deep to deep soils.

Table 4 Runoff curve numbers (CN) for the watershed area.

Cover type and hydrologic condition	CN for hydrologic soil group (A)	Occupied area in the river basin (%)
Open space (lawns, parks, golf courses)	49	14
Impervious areas (streets, roofs, paved areas, etc.)	98	45
Pasture, grassland	49	26
Woods	45	15
Average CN for the entire river basin	70.45	100

In Table 4, an approximate average Curve Number (CN) is calculated based on TR-55 (Tables 2-2a to 2-2d) for the catchment area. With this CN value, the potential maximum retention (S) can be calculated using Equation 13, as follows:

(13)

Hence, employing Equation 14, where initial abstraction (I_a) equals 0.2 times the initial abstraction potential (S), amounting to 21.3 mm, the estimated event direct runoff can be computed. In the absence of precise rainfall measurements, the SCS 24-hour rainfall with a type II distribution (characterized by short duration and high intensity) was utilized to construct a rainfall hyetograph for the day of the event, totalling 144 mm, enabling the prediction of storm runoff accordingly (Ahmed et al. 2021).

(14)

The only unknown parameter for calculating the peak discharge is the unit peak discharge (q_u). Values of q_u can be obtained by using the graphs shown in TR-55. It's important to choose the correct rainfall distribution type, which is determined from the map provided in TR-55. For Abuja, Type II rainfall distribution (most intense short-duration rainfall), which was developed by NRCS, is most like the rainfall type. Given that the time of concentration (T_c) for the watershed area above the point of analysis has been calculated as 6 hours. Based on this information, achieving the result of   is feasible through either Equation 12 or Exhibit 4-11 in TR-55.

Finally, the peak runoff (q_p) can be calculated using Equation 15:

(15)

The peak discharge calculations thus far have been conducted for September 2022, one of the rainiest months of the year. By correlating the monthly rainfall data provided in Figure 1, potential peak discharge amounts were estimated for June (171.09 mm), July (190.92 mm), August (229.15 mm), and September (241.23 mm) using Manning’s equation, KWP, and NRCS-CN methods. Calculated peak discharge amounts derived from the methods are presented in Table 5.

Table 5 Peak discharge results were obtained from three different models.

Month	Average precipitation (mm)	Manning’s Equation (m3/s)	Kinematic Wave Parameter (m3/s)	NRCS-CN method (m3/s)
June	171.09	86.75	86.90	199.84
July	190.92	104.48	104.67	247.31
August	229.15	142.60	142.85	344.62
September	241.23	155.71	155.98	376.80

Table 5 presents a comparative analysis of peak discharge estimates derived from three different methods—Manning’s equation, the Kinematic Wave Parameter method, and the NRCS-CN Method—based on the average precipitation data for June, July, August, and September. Each method yields varying peak discharge values across the months, reflecting their unique approaches to hydrological modeling. Manning’s equation and the Kinematic Wave Parameter method produce relatively similar peak discharge estimates. Because the kinematic wave model uses Manning’s equation as its momentum equation (Hosseini et al. 2018; Vatankhah 2020), simplifying the flow analysis. At the same time, the NRCS-CN Method tends to yield higher values, which is particularly evident during the peak rainfall month of September. This is because the NRCS-CN method accounts for a variety of factors, such as land cover (Zhang 2019), soil group (Barker and Chandrakantha 2022), and soil moisture conditions (Sharma et al. 2022), which result in a higher estimation of runoff and, consequently, peak discharge during intense rainfall events.

Since there are no measurement stations in the Wupa River basin and no previous studies on the river, the calculated values in Table 5 were validated by comparing them with data from the Gurara River's measuring station at Jere (Mudashiru et al. 2018), one of the nearest rivers to the Wupa River. The validation process involved establishing a regional relationship between the Gurara River at Jere (watershed area: 4,016 km²) and the Wupa River at the Nile University of Nigeria campus (watershed area: 192 km²). The physical and geological similarities between the two river watersheds made the Gurara River data a reasonable basis for comparison.

However, there are key differences to consider. The Wupa River flows through the urbanized area of Abuja, the capital city of Nigeria, before merging with the Gurara River. In contrast, the Gurara River flows through rural areas with little to no urban development. Additionally, the two basins have significantly different sizes. Urban areas typically generate 2 to 4 times higher peak flows than rural areas due to factors such as increased impervious surfaces and faster runoff response (Feng et al. 2021; Pema et al. 2019; Zimmermann et al. 2016). This accounts for the significantly higher specific discharge values (m³/s/km²) observed for the Wupa River. Table 6 highlights that the specific discharge values for the Wupa River were notably higher than those for the Gurara River.

Table 6 Comparison of calculated peak discharges with regional scaling estimates for the Wupa River.

River	Analysis type	Catchment area (km²)	Peak discharge (m³/s)	Specific discharge (m³/s/km²)
Gurara	100-year return period	4,016	1,006.79	0.251
Wupa	Manning's equation	192	155.71	0.811
Wupa	Kinematic Wave Parameter	192	155.98	0.812
Wupa	NRCS-CN	192	376.80	1.962

The Manning's equation and KWP results (approximately 156 m³/s) were found to be more realistic when considering the watershed characteristics and regional hydrology, yielding specific discharges about 3.7 times higher than those of the Gurara River, aligning with typical urban-rural discharge ratios (2–4 times). In contrast, the NRCS-CN method's results (376.80 m³/s) appeared to overestimate peak discharge, producing specific discharges about 9 times higher than the Gurara River's values, exceeding typical urban-rural discharge ratios. The validation indicates that while the NRCS-CN method may overestimate peak flows due to its sensitivity to CN values in urban settings, Manning's equation and KWP results are within reasonable bounds for an urbanized sub-catchment of this size, supported by specific discharge comparisons and typical urban hydrological responses.

Comparing results with similar studies reveals notable consistencies while providing valuable insights specific to the Wupa River basin. The close agreement between Manning's equation and KWP results (variance less than 0.2%) parallels findings from Vatankhah (2020), who noted that kinematic wave models typically use Manning's equation as their momentum equation. Meanwhile, Musthofa et al. (2019) observed in the Karajae Watershed that Manning's method produced significantly lower peak discharge estimates than other approaches, similar to observations in this study. The findings align with Walega et al. (2020), who emphasized the potential underestimation in some watershed models and highlighted the importance of adapting parameters for more accurate runoff predictions, which explains the variations in peak discharge values across different methods.

The NRCS-CN method differs from other approaches in this study due to its thorough consideration of watershed conditions. In the Izmit Basin study (Topçuoğlu et al. 2023), SCS-CN estimates indicated that about 41–42% of annual rainfall directly contributed to streamflow. In another study, Ye et al. (2018) discussed the limitations of Manning's formula, noting that it is valid under equilibrium conditions rather than extreme conditions. This distinction explains why Manning's method may yield different results than NRCS-CN. Kencanawati et al. (2023) emphasized the importance of incorporating local factors in peak discharge estimations, which complements the NRCS-CN method's more comprehensive approach. Similarly, Alkan (2022) demonstrated that watershed characteristics significantly influence peak discharge results, supporting the conclusion that while Manning's equation and KWP provide similar estimates suitable for channel flow assessment, the NRCS-CN method offers more conservative estimates for flood management in rapidly urbanizing watersheds like the Wupa River basin.

To provide a clearer understanding of the differences and similarities between the hydrological methods used in this study, a detailed comparison is presented in Table 7. This table highlights the key parameters, assumptions, input requirements, applicability, strengths, and limitations of Manning’s equation, the Kinematic Wave Parameter (KWP) model, and the NRCS-CN method. This table provides a comprehensive comparison of the techniques, helping readers to understand the contexts in which each method is most applicable and their respective strengths and limitations.

Table 7 Comparative analysis of hydrological methods.

Parameter/aspect	Manning’s equation	Kinematic Wave Parameter (KWP)	NRCS-CN method
Assumptions	Uniform flow	Simplified St. Venant equations	Empirical relations
Input Requirements	Channel geometry, slope, roughness coefficient	Channel geometry, slope, roughness coefficient	Curve number, rainfall data, soil type
Applicability	Open channels with uniform flow	Open channels and overland flow	Watersheds with varying soil types
Strengths	Simple, widely used	Accurate for various conditions	Accounts for soil and land use
Limitations	Assumes uniform flow	Requires accurate channel data	Assumes spatial uniformity of parameters

The relationship between flood risk assessment and determined peak discharges is crucial for understanding and mitigating potential hazards. When the cross-sectional area of a river decreases, particularly in proximity to residential areas, the risk of flooding escalates significantly. This reduction in area may lead to overflow beyond the riverbank, posing a severe threat to nearby residential communities. In our observation, we noted instances where during peak flow, the river surged beyond its usual confines, encroaching upon residential properties. It's important to note that in this study, calculations were based on the full capacity flow of households, rather than considering flood scenarios alone. This comprehensive approach enables a more accurate assessment of flood risks and aids in the development of effective mitigation strategies to safeguard communities against potential inundation.

4 Conclusion

This study enhances understanding of flood risk assessment through detailed analysis of the Wupa River basin in Nigeria. The comparative application of three hydrological models revealed that Manning's equation and the Kinematic Wave Parameter (KWP) model produced consistent results (approximately 156 m³/s for September), while the NRCS-CN method generated significantly higher values (376.80 m³/s).

Validation against Gurara River data demonstrated that Manning's equation and KWP results align with expected urban-rural discharge ratios, showing specific discharges approximately 3.7 times higher than the rural Gurara basin. This aligns with established research showing urban areas typically generate 2–4 times higher peak flows than rural areas.

Several methodological limitations affect these findings: application of US-based TR-55 formulas may not fully represent West African conditions; reliance on dated soil geological data introduces potential inaccuracies in CN value estimation; and the NRCS-CN method's known limitations in assessing runoff in flat, forested watersheds affect 15% of the study area (Walega et al. 2020).

The scientific value of this research lies in establishing a quantitative foundation for flood prediction in the rapidly urbanizing Wupa River basin. Our findings demonstrate the effectiveness of Manning's equation and KWP for urban watershed analysis in African contexts, where such studies remain limited. The practical applicability includes improved flood risk assessment for urban planning and infrastructure development in Abuja.

Future research should focus on developing region-specific rainfall distribution models and updating soil geological data to enhance prediction accuracy for West African watersheds.

References

1. Ahmed, M.A., A.T. Olowosulu, B.K. Adeogun, A.A. Murana, H.A. Ahmed, and I.M. Sanni. 2021. “Development of Rainfall Intensity-Duration-Frequency (IDF) Curve for Abuja, Nigeria.” Nigerian Journal of Technology 40 (1): 154–160. https://doi.org/10.4314/njt.v40i1.20
2. Aladejana, O. 2021. “Flood investigation and adaptation strategies through best management practices in an ungauged basin in Southwest Nigeria.” African Geographical Review 40 (2): 141–162. https://doi.org/10.1080/19376812.2020.1782235
3. Alkan, Ç. 2022. “Use of the WinTR-55 Hydrologic Model on Determination of Flood Peak Discharge: The Case of Kirklareli Vize Stream and Samsun Minoz Stream Watersheds.” Doğal Afetler ve Çevre Dergisi 8 (2): 305–316. https://doi.org/10.21324/dacd.1040189
4. Arcement, G.J. and V.R. Schneider. 1989. “Guide for selecting Manning’s roughness coefficients for natural channels and flood plains.” Water Supply Paper 2339, 38. https://doi.org/10.3133/wsp2339
5. Balogun, S. and T.C. Ogwueleka. 2021. “Coliforms removal efficiency of Wupa wastewater treatment plant, Abuja, Nigeria.” Energy Nexus 4, 100024. https://doi.org/10.1016/j.nexus.2021.100024
6. Bao, H., L. Wang, K. Zhang, and Z. Li. 2017. “Application of a developed distributed hydrological model based on the mixed runoff generation model and 2D kinematic wave flow routing model for better flood forecasting.” Atmospheric Science Letters 18 (7): 284–293. https://doi.org/10.1002/asl.754
7. Barker, R.D. and G. Chandrakantha. 2022. “Estimation of Runoff Potential using Curve Number Method.” Indian Journal of Ecology 49 (5): 1843–1847. https://indianecologicalsociety.com/wp-content/themes/ecology/volume_pdfs/1664681928.pdf
8. Bouabdellah, G. 2022. “Estimation of River Discharge Outside the Regime of Uniform Flow.” Periodica Polytechnica Mechanical Engineering 66 (3): 197–206. https://doi.org/10.3311/PPme.18945
9. Chin, D.A. 2020. Water-Resources Engineering (Fourth Edition). University of Miami, Pearson Education Inc., Hoboken, NJ, USA.
10. Chow, V.T., D.R. Maidment, and L.W. Mays. 1988. Applied Hydrology. McGraw-Hill Book Company, Singapore.
11. Cronshey, R. 1986. Urban hydrology for small watersheds (TR No. 55). US Department of Agriculture, Soil Conservation Service, Engineering Division. (Second Edition), Washington, D.C.
12. Echendu, A.J. 2020. “The impact of flooding on Nigeria’s sustainable development goals (SDGs).” Ecosystem Health and Sustainability 6 (1): 1791735. https://doi.org/10.1080/20964129.2020.1791735
13. Echendu, A.J. 2023. “Flooding and Waste Disposal Practices of Urban Residents in Nigeria.” GeoHazards 4 (4): 350–366. https://doi.org/10.3390/geohazards4040020
14. ESDAC. 1990. “Soils map of Nigeria [Official].” Soil Survey Division, Federal Department of Agricultural Land Resources (FDALR), Kaduna, Nigeria. https://esdac.jrc.ec.europa.eu/content/soils-map-nigeria-0
15. Eshghizadeh, M. 2024. “Urban development scenarios on flood peak discharge in an arid urban watershed using the WinTR-55 hydrologic model.” International Journal of Human Capital in Urban Management 9 (2–34): 345–356. https://doi.org/10.22034/IJHCUM.2024.02.11
16. Ezemonye, M.N., C.N. Emeribe, and N.C.R. Anyadike. 2016. “Estimating stream discharge of Aboine River Basin of Southeast Nigeria using modified Thornthwaite climatic water balance model.” Journal of Applied Sciences and Environmental Management 20 (3): 760. https://doi.org/10.4314/jasem.v20i3.30
17. Feng, B., Y. Zhang, and R. Bourke. 2021. “Urbanization impacts on flood risks based on urban growth data and coupled flood models.” Natural Hazards 106, 613–627. https://doi.org/10.1007/s11069-020-04480-0
18. Hosseini, S.M., B. Ataie-Ashtiani, and C.T. Simmons. 2018. “Density-based global sensitivity analysis of sheet-flow travel time: Kinematic wave-based formulations.” Journal of Hydrology 559, 556–568. https://doi.org/10.1016/j.jhydrol.2018.02.052
19. Ibangha, I-A.I., S.N. Madueke, S.O. Akachukwu, S.C. Onyeiwu, S.C. Enemuor, and V.N. Chigor. 2024. “Physicochemical and bacteriological assessment of Wupa wastewater treatment plant effluent and the effluent-receiving Wupa River in Abuja, Nigeria.” Environmental Monitoring and Assessment 196, 30. https://doi.org/10.1007/s10661-023-12209-2
20. Ibrahim, S., B. Brasi, Q. Yu, and M. Siddig. 2022. “Curve number estimation using rainfall and runoff data from five catchments in Sudan.” Open Geosciences 14 (1): 294–303. https://doi.org/10.1515/geo-2022-0356
21. Idowu, D., B.G. Peter, J. Boakye, S. Cohen, and E. Carter. 2025. “Evaluating Earth observation products for Catchment-Scale operational flood monitoring and risk management in a sparsely gauged to ungauged river basin in Nigeria.” International Journal of Applied Earth Observation and Geoinformation 138, 104445. https://doi.org/10.1016/j.jag.2025.104445
22. Igbokwe, E.C., S. Musa, K. Anienwe, A.O. Oliha, and P.C. Anyadiegwu. 2024. “A GIS-Based Approach for Assessing Urban Development Potential in Federal Capital Territory Nigeria.” Asian Journal of Geographical Research 7 (3): 94–114. https://doi.org/10.9734/ajgr/2024/v7i3244
23. Isagba, E.S., O.C. Izinyon, C.N. Emeribe, N.O. Uwadia, and C.U. Ezeh. 2021. “Estimation of stream discharge of ungauged basins using NRCS-CN and remote sensing methods: A case study of Okhuwan and Okhaihe catchments, Benin City, Edo State, Nigeria.” International Journal of Water Resources and Environmental Engineering 13 (3): 165–183. https://doi.org/10.5897/IJWREE2021.1014
24. Kästner, K., A.J.F. Hoitink, P.J.J.F. Torfs, B. Vermeulen, N.S. Ningsih, and M. Pramulya. 2018. “Prerequisites for Accurate Monitoring of River Discharge Based on Fixed‐Location Velocity Measurements.” Water Resources Research 54 (2): 1058–1076. https://doi.org/10.1002/2017WR020990
25. Kencanawati, M., D. Iranata, and M.A. Maulana. 2023. “Hydrologic Modeling System HEC-HMS Application for Direct Runoff Determination.” Journal of Human, Earth, and Future 4 (2): 153–165. https://doi.org/10.28991/HEF-2023-04-02-02
26. Koko, A.F., W. Yue, G.A. Abubakar, A.A.N. Alabsi, and R. Hamed. 2021. “Spatiotemporal Influence of Land Use/Land Cover Change Dynamics on Surface Urban Heat Island: A Case Study of Abuja Metropolis, Nigeria.” ISPRS International Journal of Geo-Information 10 (5): 272. https://doi.org/10.3390/ijgi10050272
27. Korenic, R. 2022. Mahoning County Drainage Criteria and Storm Water Manual. Mahoning County Engineers Office, Mahoning County, Ohio, USA. https://www.mahoningcountyoh.gov/DocumentCenter/View/103/Storm-Water-Manual-with-Cover-PDF?bidId=
28. Kumar, V. 2020. “A Study of Travel Time for Different Open Channels.” Journal of the Institution of Engineers (India): Series A 101, 399–407. https://doi.org/10.1007/s40030-020-00439-3
29. Lamine, B.O.M., V.G. Ferreira, Y. Yang, C.E. Ndehedehe, and X. He. 2021. “Estimation of the Niger River cross-section and discharge from remotely-sensed products.” Journal of Hydrology: Regional Studies 36, 100862. https://doi.org/10.1016/j.ejrh.2021.100862
30. Meshram, S.G., S.K. Sharma, and S. Tignath. 2017. “Application of remote sensing and geographical information system for generation of runoff curve number.” Applied Water Science 7, 1773–1779. https://doi.org/10.1007/s13201-015-0350-7
31. Metselaar, K. 2023. “The NRCS curve number equation derived from an instantaneous unit hydrograph: Some consequences.” Journal of Hydrology X 19, 100151. https://doi.org/10.1016/j.hydroa.2023.100151
32. Mir, A.A. and M. Patel. 2024. “Machine learning approaches for adequate prediction of flow resistance in alluvial channels with bedforms.” Water Science & Technology 89 (2): 290–318. https://doi.org/10.2166/wst.2023.396
33. Mudashiru, R.B., A.W. Salami, and S.O. Bilewu. 2018. “Evaluation of Methods of Peak Runoff Determination using Catchment Characteristics for Jere Sub-basin, Gurara River Basin, North Central Nigeria.” The Journal of Engineering Research [TJER] 15 (1): 5. https://doi.org/10.24200/tjer.vol15iss1pp26-41
34. Musthofa, F., A. Brilianty, H. Setyowati, K.S. Wati, M.R. Afani, N.U. Agustin, and S.H. Murti. 2019. “The Water Discharge Peak Estimation Based on Runoff Coefficient Number Using Raster Based Hassing and Cook Method in Karajae Watershed, South Sulawesi Province.” In: The 6th Geoinformation Science Symposium, Proceedings of SPIE—the International Society for Optical Engineering 2019, 31–40.
35. NRCS. 2022. National Engineering Handbook: Part 630—Hydrology. Independently published (September 29, 2022).
36. Okacha, A., A. Salhi, M. Bouchouou, and H. Fattasse. 2024. “Enhancing flood forecasting accuracy in data-scarce regions through advanced modeling approaches.” Journal of Hydrology 645 (B): 132283. https://doi.org/10.1016/j.jhydrol.2024.132283
37. Oladokun, V.O. and D. Proverbs. 2016. “Flood risk management in Nigeria: A review of the challenges and opportunities.” International Journal of Safety and Security Engineering 6 (3): 485–497. https://doi.org/10.2495/SAFE-V6-N3-485-497
38. Park, M., J. Jung, H. Joo, Y. Kim, J. Kwak, J. Kim, C. Choi, and H.S. Kim. 2021. “A synthetic equation for storage function model parameter estimation based on kinematic wave approximation.” Hydrological Sciences Journal 66 (3): 544–554. https://doi.org/10.1080/02626667.2021.1877707
39. Pema, K., N. Kumar, B. Tayeng, and K. Danggen. 2019. “State Disaster Management Plan-2019.” Department of Disaster Management Government of Arunachal Pradesh. https://sdma-arunachal.in/wp-content/uploads/2020/08/SDMP-2019.pdf
40. Salah Abd Elmoaty, M. and T.A. El-Samman. 2020. “Manning roughness coefficient in vegetated open channels.” Water Science 34 (1): 124–131. https://doi.org/10.1080/11104929.2020.1794706
41. Samarinas, N. and C. Evangelides. 2021. “Discharge estimation for trapezoidal open channels applying fuzzy transformation method to a flow equation.” Water Supply 21 (6): 2893–2903. https://doi.org/10.2166/ws.2021.155
42. Sharma, I., S.K. Mishra, A. Pandey, and S.K. Kumre. 2022. “A modified NRCS-CN method for eliminating abrupt runoff changes induced by the categorical antecedent moisture conditions.” Journal of Hydro-Environment Research 44, 35–52. https://doi.org/10.1016/j.jher.2022.07.002
43. Singh, V.P. and V.T. Chow. 2017. Handbook of Applied Hydrology (Second Edition). Available online at McGraw-Hill Education.
44. Smith, J.A., A.A. Cox, M.L. Baeck, L. Yang, and P. Bates. 2018. “Strange Floods: The Upper Tail of Flood Peaks in the United States.” Water Resources Research 54 (9): 6510–6542. https://doi.org/10.1029/2018WR022539
45. Stein, K., D. Coulibaly, L.H. Balima, D. Goetze, K.E. Linsenmair, S. Porembski, K. Stenchly, et al. 2020. “Plant-Pollinator Networks in Savannas of Burkina Faso, West Africa.” Diversity 13 (1): 1. https://doi.org/10.3390/d13010001
46. Topçuoğlu, M.E., R. Karagüzel, and A. Doğan. 2023. “Comparison of the SCS-CN and Hydrograph Separation Method for Runoff Estimation in an Ungauged Basin: The Izmit Basin, Turkey.” International Journal of Economic and Environmental Geology 12 (4): 22–31. https://doi.org/10.46660/ijeeg.v12i4.70
47. Umar, N. and A. Gray. 2023. “Flooding in Nigeria: A review of its occurrence and impacts and approaches to modelling flood data.” International Journal of Environmental Studies 80 (3): 540–561. https://doi.org/10.1080/00207233.2022.2081471
48. Vatankhah, A.R. 2020. “Open-channel sections with constant kinematic wave parameters.” ISH Journal of Hydraulic Engineering 26 (3): 319–324. https://doi.org/10.1080/09715010.2018.1491332
49. Vatankhah, A.R. 2023. “Uniform flow depth in trapezoidal open channels.” Flow Measurement and Instrumentation 94, 102458. https://doi.org/10.1016/j.flowmeasinst.2023.102458
50. Walega, A., D.M. Amatya, P. Caldwell, D. Marion, and S. Panda. 2020. “Assessment of storm direct runoff and peak flow rates using improved SCS-CN models for selected forested watersheds in the Southeastern United States.” Journal of Hydrology: Regional Studies 27, 100645. https://doi.org/10.1016/j.ejrh.2019.100645
51. Wang, B., Y. Chen, C. Wu, J. Dong, X. Ma,and J. Song. 2016. “A semi‐analytical approach for predicting peak discharge of floods caused by embankment dam failures.” Hydrological Processes 30 (20): 3682–3691. https://doi.org/10.1002/hyp.10896
52. World Bank. 2024. World Bank Climate Change Knowledge Portal. Available online: https://climateknowledgeportal.worldbank.org/
53. Ye, A., Z. Zhou, J. You, F. Ma, and Q. Duan. 2018. “Dynamic Manning’s roughness coefficients for hydrological modelling in basins.” Hydrology Research 49 (5): 1379–1395. https://doi.org/10.2166/nh.2018.175
54. Zhang, W-Y. 2019. “Application of NRCS-CN method for estimation of watershed runoff and disaster risk.” Geomatics, Natural Hazards and Risk 10 (1): 2220–2238. https://doi.org/10.1080/19475705.2019.1686431
55. Zheng, H., E. Huang, and M. Luo. 2020. “Applicability of Kinematic Wave Model for Flood Routing under Unsteady Inflow.” Water 12 (9): 2528. https://doi.org/10.3390/w12092528
56. Zimmermann, E., L. Bracalenti, R. Piacentini, and L. Inostroza. 2016. “Urban Flood Risk Reduction by Increasing Green Areas for Adaptation to Climate Change.” Procedia Engineering 161, 2241–2246. https://doi.org/10.1016/j.proeng.2016.08.822