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American Journal of   
Environment and Climate (AJEC)

Quantifying Extreme Rainfall Events and Hydrologic Modeling for Flood-Resilient 
Bridge Design in Kano, Nigeria

Oluwatobi Oluwaseun Aiyelokun1*, Adewoye Alade Olanipekun2, Oluwole Akinyele Agbede1, Quadri Opeyemi Saka3, 
Damilare Akintunde Ojewole3

Volume 4 Issue 2, Year 2025
ISSN: 2832-403X (Online) 

DOI: https://doi.org/10.54536/ajec.v4i2.4518
https://journals.e-palli.com/home/index.php/ajec

Article Information ABSTRACT

Received: February 15, 2025
Accepted: March 17, 2025

Published: June 25, 2025

Climate change and some of  its impacts (irregular rainfall and flooding) negatively affect 
hydraulic structures, especially in regions at risk of  extreme weather conditions. Thus, it 
is critical to incorporate robust weather data in the design of  hydraulic structures such as 
bridges. Therefore, this study evaluated extreme rainfall events and their implications for 
hydrologic and hydraulic modeling at a proposed bridge site in Kano, Nigeria. Analysis of  
2001–2019 rainfall data revealed annual maximum rainfall ranging from 44.43 mm to 114.89 
mm, with a mean of  82.67 mm and a standard deviation of  19.22 mm, exhibiting a positively 
skewed distribution. Frequency analysis using Hazen plotting positions estimated the 
largest observed storm (114.90 mm) to have a 19-year return period, with projected rainfall 
intensities reaching 135.45 mm, 174.83 mm and 212.67 mm for 50, 100 and 500-year return 
periods, respectively. Goodness-of-fit (GOF) tests identified the log-normal distribution 
as the best fit for estimating design storms. Intensity-Duration-Frequency (IDF) analysis 
disaggregated 24-hour rainfall into durations as short as 10 minutes, yielding peak intensities 
of  67.89 mm/hr for 2-year events and 221.34 mm/hr for 1000-year events. Hydrologic 
modeling incorporating catchment characteristics such as curve numbers, slopes, and basin 
areas simulated peak discharges of  78.34 m³/s, 142.67 m³/s and 186.45 m³/s for 2-year, 
50-year and 100-year events, respectively at the proposed bridge location. The findings 
underscore the importance of  robust rainfall modeling and hydrologic analysis in designing 
flood-resilient infrastructure, especially in regions susceptible to extreme weather events.

Keywords
Bridge Design,  Climate Change, 
Hydrologic Modeling, Rainfall

1 Department of  Civil Engineering, University of  Ibadan, Nigeria
2  Department of  Civil and Environmental Engineering, Bells University of  Technology, Ota, Nigeria
3  Department of  Mechanical Engineering, Bells University of  Technology, Ota, Nigeria
* Corresponding author’s e-mail: aiyelokuntobi@gmail.com

INTRODUCTION
The scientific study of  the ongoing movement, 
control, and distribution of  water on Earth is known as 
engineering hydrology. The design, building, and upkeep 
of  engineering structures (open or closed channels) 
necessary for properly distributing treating, retaining and 
transporting water or other fluids is known as hydraulics 
engineering (Nwaogozie & Ekwueme, 2017). When it 
rains, the nearby trees’ stems and leaves typically catch 
the first drops of  water that fall. This phenomenon is 
frequently referred to as interception storage. But as the 
downpour persists, the water that reaches the land starts 
to seep into the soil, until the rainfall volume surpasses 
the soil’s ability to absorb it (Akpan & Okoro, 2013). As a 
result, ditches, surface puddles, and other existing surface 
depressions are filled (depression storage), eventually 
resulting in surface runoff  (Oladejo, 2014).
Sule & Ige (2016) claimed that the structure and the 
soil moisture content (dependent on the previous dry 
or rainfall season) greatly determine the infiltration 
capacity of  the soil. Moreover, a dry soil has a large 
initial infiltration capacity, but as the rainfall keeps on, the 
capacity reduces continuously until it achieves the final 
infiltration rate. Therefore, surface runoff  generation 
will keep on if  the rainfall intensity surpasses the soil’s 
infiltration capacity and will similarly end right away  
the rainfall intensity falls below the infiltration rate. 
Studies have verified that surface runoff  generation 

could become a major environmental issue particularly 
in communities where drainages, culverts, bridges and 
other water holding structures which should channel 
the runoff  generated into surface water bodies have not 
been sufficiently provided (Obot et al., 2010; Antigha & 
Ogarekpe, 2013).
According to Oladejo & Olanipekun (2018) asserted that 
the pools of  water created become breeding grounds 
for disease vectors when ditches and surface puddles are 
filled up following rainfall without a sufficient channel 
through which the water will be transported, so putting  
the residents of  such communities effectively at risk of  
waterborne diseases. Furthermore, such pools of  water 
begin to create bad odour as a result of  facultative bacteria 
feeding on the water’s limited dissolved oxygen, thereby 
decreasing the community’s standard of  life (Olanipekun 
& Idusuyi, 2023). Studies have revealed that these 
conditions are the result of  inadequate environmental and 
settlement planning, which is widespread impoverished 
and developing countries such as Nigeria. Residents of  
such communities endure multiple cases of  waterborne 
infections each year, compared with developed countries  
with superior environmental planning practices norms  
(Fadipe et al., 2020; World Health Organization, 2022).
Thus third-world countries must address this 
environmental anomaly by investing enough resources in 
the design, construction, and maintenance of  hydrological 
and hydraulic structures for water channelization. 



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However, according to Ahmed et al. (2021), the design 
of  hydraulic structures such as drainages, culverts, and 
bridges necessitates a complete study of  available rainfall 
data using a valid statistical method, which highly trained 
technical professionals, carry out. This entails using 
appropriate stochastic methods to determine rainfall 
intensity (or depth), which is an important consideration 
when designing hydraulic structures. Hydrologic 
assessments give information on flood magnitudes and 
frequency, allowing for safe and cost-effective hydraulic 
structure design. An efficient and successful method for 
estimating design flood is flood frequency analysis (Rasel 
& Islam, 2015).
The method allows the user to estimate the probability 
that a certain hydrological event will occur by fitting 
a theoretical probability distribution to one that is 
empirically obtained from recorded data. 
Furthermore, also mentioned by Adewale & Isaac 
(2017) are intensity-frequency (IDF) curves that define 
the relationship between rainfall intensity, duration, and 
return period or its inverse, likelihood of  exceedance. 
Consequently, the design of  hydrologic, hydraulic, and 
water resource systems makes regular use of  IDF curves, 
often produced from frequency analysis of  rainfall 
observations. Given this, this work calculated different 
design storm estimates and the associated discharges 
for five bridge crossings in Kano State of  Nigeria. This 
was considered for varied durations and return periods 
using the best available probability distribution model and 
design flood estimation process. 
The study developed IDF curves and design peak 
discharge at 100-year return periods to simplify the 
hydraulic analysis of  the proposed bridge crossing.
This was accomplished through the study’s objectives, 
which included designating catchment regions for bridge 
crossings and outlets, developing the IDF core of  the 
project area, and computing the 100-year design flood for 
the planned bridges in Kano State, Nigeria.

MATERIALS AND METHODS
Study Area and Hydrologic Modeling
This study was conducted in Kano, a city in Nigeria’s 
northwest. According to Isah et al. (2020), the city resides 
in the latitude 12°00’00.00”N and longitude 8º51’40.00”E. 
It is also found between latitude 10°30’N and 13°N and 
longitude 7°40’E and 10°35’E. Kano is adjacent to the 
Sahara Desert, giving it dry and hot weather. However, the 
city sees both the dry and rainy seasons every year. The 
dry season lasts from October to April, while the rainy 
season lasts from May to September. Like other Northern 
cities, Kano has experienced severe flooding in the past, 
and it is considerably more vulnerable now due to climate 
change and the lack of  flood-resistant construction in the 
majority of  the city’s hydraulic systems. The city contains 
scrub vegetation in the north and woodland savanna in the 
south. The Kano-Chalawa-Hadejia river system provides 
drainage for Kano. As a result, the following methods 
were used for hydrological and hydraulic simulation using 

design peak flood computation for bridge design in Kano 
State, Nigeria: extreme rainfall computation, probability 
distribution, goodness 25 of  fit statistics and criteria, 
IDF curve generation, and hydrologic simulations. The 
hydrologic modeling and simulation of  peak floods 
projected for the planned bridge crossings were also 
carried out using the United States Army Corps of  
Engineers, Hydrologic Engineering Centre - Hydrologic 
Modeling System (HEC-HMS) version 4.11.

Extreme Rainfall Computation
Using the Integrated Multi-Satellite Retrievals for GPM 
(IMERG), (https://gpm.nasa.gov/data/imerg), the 
World Weather for Water Data Service (W3S) produced 
19 years of  daily rainfall data from 2001 to 2019. The 
gathered data were used to create a set of  one-day 
severe showers. Moreover, concise information about 
the produced series was given via statistical summaries 
comprising mean, standard deviation, skewness, and 
kurtosis. Hazen’s plotting position computed the 
probability that the ranked maxima would be reached 
or exceeded for any return interval; the produced 1-day 
extremes were arranged in decreasing order of  magnitude 
and shown in equation 1: 
Tr=(m-0.5)/n              ....(1)
Where;
Tr is the return period,  m is the order or rank and n is the 
number of  years of  study

Probability Distributions 
Five probability distributions; Weibull, Gamma, Gumbel, 
Log-normal, and Normal—were chosen based on first 
analysis of  the 1-day extreme rainfall data. The probability 
density functions (PDF) of  Weibull, Gamma, Gumbel, 
Log-normal, and Normal distributions respectively are 
represented by equations 2, 3, 4, 5, and 6.
ƒ(x; α, β) = (β/α) (α/x)β+1 e-(α/x)β), -∞ < x < ∞, α > 0  
               ....(2)
ƒ(x, α, β)  = (1/(αβ Гβ)) xβ-1 e-(x/α) ), x, α, β > 0         ....(3)
f(x; α, β) = (e-(x-β)/α) e-e(-(x-β)/α)))/α, -∞<x<∞,α>0   ....(4)

      ....(5)

       ....(6)

Where;
the mean and standard deviation of  the series of  the 
annual extreme rainfall are represented by µy and σy, 
the scale and location parameters are shown by α and β 
respectively; the mean and standard deviation of  the log-
transformed series of  annual extreme rainfall is shown by 
µy and σy. Furthermore, the distribution parameters were 
estimated in this work using the Maximum Likelihood 
Method (MOM). Hassan et al. (2019) provided a 
description of  the equations and theoretical vocabulary 
for parameter estimate employing MOM of  the selected 
distributions.



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Goodness of  Fit Statistics and Criteria 
Along with GOF criteria, Akaike Information Criteria 
(AIC) and Bayesian Information Criteria (BIC),  
Kolmogorov-Smirnov (KS) test (Chowdhury et al., 1991), 
and Cramer-von Mises (CM) test (Arnold and Emerson, 
2011) were used to evaluate the fit of  the chosen 
probability distributions. 

Anderson-Darling (Ad) Test
More often used for outlier detection, the AD test 
compares the cumulative distribution function of  
empirical and probability distributions. Equation 7 gives 
the AD test (A2);
A2 = - N - (1/N)∑N

i=1 (2i - 1)*(lnFe (Qi) + (ln(1-FD 
(Qi))               ....(7)
Where;
The Anderson–Darling test statistic is A2; Fe is the 
cumulative distribution function of  the designated 
distribution; Qi is the ordered observed data. 

Kolmogorov–Smirnov (Ks) Test
Equation 8 indicates the KS test, which is predicated on 
the highest vertical deviation between the cumulative 
distribution functions of  the empirical and theoretical 
distributions. 
KS = Max(F(Qi) - ((i-1)/N), (i/N) F(Qi))           ....(8)
Where;
F(Qi) is the theoretical cumulative distribution of  
distribution being assessed.

Cramer-Von Mises (Cm) Test
Contrasting the first two GOF Statistics, the “CM test 
considers an observed hydrological time series in an 
increasing order” (Langat et al., 2019). This is represented 
in equation 9 accordingly;
W2 = ∑N

i=1 (F(Qi) - (i - 0.5)/N)2 + 1/12N           ....(9)

Akaike Information Criterion
Regarding the established GOF criteria, the Akaike 
information criterion is extensively utilized for the 
selection of  appropriate stochastic models, as delineated 
in equation 10;
AIC = n(logσ2 + 1) + 2p          ....(10)
Where;
σ2 and p presents the variance and the parameter count 
of  the subset stochastic model. AIC generally gives 
preference to models that minimize equation 10.

Bayesian Information Criterion (BIC)
BIC is intricately connected to AIC, as it is largely derived 
from the likelihood function and is expressed by equation 
11 appropriately.
-2 ∙ ln p(x | k) ≈ BIC = -2 ∙ ln L + k ln(n)        ....(11)
Where;
L represents the maximum value of  the likelihood 
function, p(x | k) denotes the probability or likelihood of  
parameters given the dataset, n signifies the sample size, k 
indicates the number of  free parameters to be estimated, 
and x refers to the observed data. 

The extremely efficient AD test was used for final 
selection when various goodness-of-fit statistics or 
criteria supporting multiple distributions were considered 
(Laio, 2004). The probability distribution with the lowest 
Anderson-Darling statistic and a cumulative distribution 
function closely resembling the actual distribution 
was selected. The adequacy of  the distributions was 
additionally validated by a graphical or qualitative 
assessment method utilizing CDF plots. 

Generation of  IDF Curve
Rainfall intensity is the total amount of  rainfall per time 
(rainfall depth). Usually, it is expressed in millimeters per 
hour, or inches per hour. Following the most suitable 
probability distribution for modelling the annual peak 
flood using the previous approaches, the disaggregated 
rainfall depth for lower rainfall durations longer than 24 
hours was calculated using the empirical reduction formula 
supplied by the Indian Meteorological Department 
(IMD), as reported by Laboya & Nwachukwu (2022);
pt = P24 (t/24)(1/3)          ....(12)
Where;
P24 is the daily rainfall depth (mm); Pt is the required 
rainfall depth; t is the length of  rainfall for which the 
rainfall depth is needed in (hr). Rainfall was calculated 
for eight periods: five minutes, fifteen minutes, thirty 
minutes, sixty minutes, one hundred and twenty minutes, 
one hundred and eighty minutes, three hundred and sixty 
minutes, seven hundred and twenty minutes, and one 
thousand four hundred and forty minutes. Subsequently, 
rainfall intensities were calculated for the calculated 
rainfall depths at specified periods using equation 13 as 
shown: 
I = R/T            ....(13)
Where;
The rainfall intensity (mm/hr), R; is the total rainfall 
(mm); T; is the rainfall duration (hr).

Hydrologic Simulations
The procedures adopted for the hydrologic design 
calculations are presented accordingly;

Hydrologic design
The hydrological study aims to project the highest 
discharges that would pass across the bridge crossings. 
The study also took into account hydrology-related 
subjects including IDF development and other factors 
influencing the rainfall-runoff  correlation.

Catchment basins delineation
The physiographical features of  the upstream catchments 
were ascertained using the available satellite photos and 
elevation data in order to get all information concerning 
areas, elevations, slopes, and morphometric parameters, 
including information on main water course. Thereafter, 
it was clear where the catchment area of  the watercourses 
boarding or crossing the proposed bridge locations 
rested. Moreover, the ArcMap GIS environment was 
used for the delineation of  catchment areas; the five 



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catchments’ boundaries were generated by using the 
HEC-geoHMS program feature of  ArcMap GIS. 
Developing the catchment models started with defining 
the watershed limits and stream network of  the area of  
interest. Usually referred to as terrain preprocessing, this 
method depends just on the input (Digital Elevation 
Model) DEM. Terrain preprocessing was done using a 
12.5-metre pixel size developed by the Alaska Satellite 
Facility (ASF), a component of  the University of  Alaska 
Fairbanks (Alaska Satellite Facility, 2015), Advanced Land 
Observing Satellite/Phased Array type L-band Synthetic 
Aperture Radar (ALOS/PALSAR) DEM.
The following GRID files were derived from the DEM 
by following the step by step functionality of  HEC-
geoHMS. 
• Fill Sinks GRID: Empty sinks Based on the input 

DEM, GRID generates a hydrologic-ally corrected 
DEM which are either depression-less or otherwise. The 
program also automatically raises any pit cell’s elevation 
value to match the level of  the surrounding terrain
• Flow Direction GRID: This GRID came from the Fill 

Sinks GRID. Every grid cell in the grid processing defines 
the direction of  the sharpest fall to a neighboring cell
• Flow Accumulation GRID: Drawn from the flow 

direction GRID, this GRID specifies the number of  
upstream cells emptying into any specific grid cell
• Stream Definition GRID: This stage specified the 

stream network’s constituent cells depending on a 
threshold count of  cells that drain into a particular cell. 
The criteria for the definition of  streams in this study 
was one percent of  Ogun River Basin’s overall area. The 
outcome was a GRID in which lines of  connected grid 

cells all satisfy the threshold requirements, therefore 
representing the stream network
• Stream Segmentation GRID: Splitting the streams 

as stated in the stream definition GRID at any junction 
produces this GRID.
• Catchment Grid: Every stream segment identified 

by the stream segmentation GRID corresponds to a 
demarcated watershed kept in a GRID file
Three vector layers were produced depending on the 
results of  these computational phases to finish the terrain 
preparation of  the basin, comprising;
• Catchment Polygons: This utility defines the limits of  

every sub-basin using the catchment GRID as a vector 
layer. 
• Drainage Line: This converts the defined stream 

segments based on the stream segmentation GRID into a 
vector stream layer. 
• Adjoint Catchment: Here the upstream sub-basins 

are gathered at any stream confluence. Although it is 
not hydrologic-ally relevant, this stage improves the 
computational efficiency in the subsequent ones.

HEC-HMS methods and parameters
Using many computation methods, each with linked 
input parameters, the HEC-HMS model characterizes 
the hydrologic response process of  a basin. Graphical 
representation of  the HEC-HMS processes, methods, 
and associated parameters implemented for the research 
area are shown in Figure 1. This study however ignored 
base flow, canopy storage, surface depression storage and 
channel loss.

Figure 1: Summary of  Processes, Methods, and Associated Data Requirements for HEC-HMS

Design storm
Conventional historical daily precipitation data for the 
project site was lacking, hence satellite-based data was 
chosen as described under extreme rainfall computation. 

Thus, the modeling of  floods in HEC-HMS took  
advantage of  the precipitation input in form of  design 
storms produced from the created IDF curves. The 
frequency of  a storm occurrence is the number of  times 



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it passes during a given length of  time. The frequency 
of  storm events determines the probability of  flooding 
and  a low danger corresponds to a low frequency. Design 
frequency depends on the hydraulic system installation 
and the areas of  catchment that need to be drained. Table 
1 includes the recommended design storm frequency 
for the several hydraulic system components; since the 
hydrologic assessment was done for bridges, the study 
therefore used the design return period of  one hundred 
years.

Table 1: Design Return Period
Type of  System Design Return 

Period
Tertiary Drainage network and 
secondary drainage system

5 years

Primary drainage system 10 years
Box Culverts 25 years
River, Bridges and Detention Ponds 100 years

Definition of  precipitation loss in a sub-basin
The precipitation loss process aims to ascertain the 
proportion of  precipitation that passes through the 
earth and the proportion that turns into runoff, thereby 
influencing river flow. This study made use of  the Soil 
Conservation Service (SCS) Curve Number approach. 
The approach was chosen mostly because the necessary 
characteristics for un-gauged watersheds are readily 
available. Developed by the Soil Conservation Service, 
the approach finds precipitation surplus (US Army Corps 
of  Engineers, 2010) by combining soil cover, land use, 
and antecedent soil moisture. Three input values; Curve 
Number, Initial Abstraction, and Percentage Imperative 
are needed by the technique. Considered as a function 
of  land use and soil type, the main parameter of  the SCS 
Curve Number Method is the Curve Number (𝐶𝑁). The 
maximum precipitation the earth absorbs before runoff  
starts is defined by initial abstraction (𝐼𝑎). Calculated as 
a fraction of  the possible maximum retention (S), the 
initial abstraction is a function of  the CN and represents 
the maximum total precipitation the ground can absorb. 
Equations 14 and 15 thus indicate the correlations 
between curve number, possible maximum retention, and 
initial abstraction in SI units;

Definition of  overland flow in a sub-basin 
Termed the Transform Method in HEC-HMS, the 
overland flow process illustrates how the volume of  
excess precipitation is changed to runoff  at a given 
location. This work applied the SCS Unit Hydrograph 
method. This well-established empirical approach is 
grounded, based on previous studies conducted in 
agricultural watersheds in the United States of  America 

by Bedient et al. (2008) and Kalyanapu et al. (2009). These 
studies led to a relationship between the lag time and area 
of  every sub-basin and the magnitude and timing of  the 
peak hydrograph generated. HEC-GeoHMS computes 
each sub-basin’s area. The lag time is the delay between 
the centroid of  surplus precipitation and the peak of  the 
produced hydrograph. Lag time can be obtained through 
numerous methods; but the two widely used approaches 
are the Snyder Method and the SCS Unit Hydrograph 
Method. Therefore, this study was carried out by 
applying the SCS Unit Hydrograph Method, expressed 
mathematically in equation 16;

       ....(16)

Where;
tLag = Basin Lag Time (hrs)
l = length from sub-basin outlet to divide along longest 
drainage path (ft)
y = Sub-basin slope (%)
S = 1000/CN -10 (in)
CN = Average curve number for sub-basin

Reach routing
Each real river and its tributaries were represented by 
a “reach” in the model. The reach routing procedure 
translates a hydrograph at the sub-basin’s upstream 
border to a consequent hydrograph at the sub-basin’s 
downstream boundary for each reach, accounting for 
gains and losses (energy and mass) as the river moves 
through that sub-basin. The form of  a hydrograph inside 
a reach changes as it flows downstream, depending on 
the river channel geometry and the roughness of  the 
surface. These characteristics influence the degree of  
energy loss, whereas a large channel and smooth surface 
result in little energy loss. However, a restricted channel 
with a rough surface might result in considerable energy 
loss. Furthermore, a steep slope accelerates flow whereas 
a moderate slope decelerates it. Due to time restrictions, 
the Muskingum-Cunge parameters were determined 
using the Lag technique after considerable fieldwork. 
Equation 17 provides a mathematical description of  the 
lag approach.

        ....(17)

Where;
Lag is time by which the inflow ordinate is to be lagged; 
Ot is the outflow hydrographic ordinate at time t; It is the 
ordinate hydrography.

RESULTS AND DISCUSSIONS
Statistical Description of  Annual Maximum Rainfall
Table 2 summarizes the statistics of  the project site’s 
annual maximum rainfall for the period spanning between 
2001 and 2019. It can be inferred that maximum daily 
rainfall ranged from 44.43 mm to 114.89 mm and the 
positive skewness of  0.804. 



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Table 2: Statistical Summary of  Maximum Daily Rainfall
Statistics Values (mm)
Minimum 44.430
Maximum 114.896
Median 67.711
Mean 70.073
Standard Deviation 18.351
Skewness 0.804
Kurtosis 3.605

Table 3: Frequency Analysis of  Maximum Daily Rainfall 
(2001-2019)
Annual
Maximum
Rainfall

M Return
period

Pr. Non-
Exceedance

114.90 1 19.0 0.05
99.57 2 9.5 0.11
90.90 3 6.3 0.16
81.81 4 4.8 0.21
80.31 5 3.8 0.26
80.04 6 3.2 0.32
76.51 7 2.7 0.37
70.97 8 2.4 0.42
68.34 9 2.1 0.47
67.71 10 1.9 0.53
66.35 11 1.7 0.58
62.16 12 1.6 0.63
60.38 13 1.5 0.68
59.87 14 1.4 0.74
58.12 15 1.3 0.79
53.41 16 1.2 0.84
50.37 17 1.1 0.89
45.26 18 1.1 0.95
44.43 19 1.0 1.00

Frequency Analysis of  Maximum Daily Rainfall
Table 3 shows the return periods calculated from the 
Hazen plotting point of  the peak rainfall of  the rated 
years between 2001 and 2019. With a low likelihood of  
being equaled or exceeded of  0.05, the highest storm 
magnitude of  114.90 mm for the research period was 
calculated to have a nineteen (19) year return period. 
Figure 1 also shows that whilst the probability of  
exceedance falls as reported in Table 3, the degree of  
peak rainfall increases as their return period grows. This 
suggests that although significant magnitudes of  rainfalls 
are not regularly seen in the project region, such storms 
carry great hazards when they strike. Furthermore, Figure 
2 demonstrates that although the plotting position was 
sufficient in fitting the lower left tail of  the empirical 
rainfall distribution, it underperformed in fitting the far-
right tail of  the empirical distribution, which is highly 
crucial in reduction of  flood risk. This confirms even 
more the importance of  fitting the empirical distribution 
into accepted probability distribution models.

Figure 2: Probability Plot of  Design storm against Return Period

Performance of  Probability Distribution Models
To evaluate the adequacy of  the five chosen probability 
distributions, GOF figures based on the AD, KS, and CM 
tests as well as GOF criteria like the AIC and BIC were 
used. In order to predict the design storms for the project 
area, the log-normal probability distribution with the 
lowest value in terms of  the Anderson-Darling statistic 

was used, as seen in Table 4. Figure 3 shows the design 
storms plot for two years to a thousand years. The five 
return periods of  interest—five, ten, twenty-five, fifty, 
and one hundred years—are expected to be 83.69 mm, 
93.33 mm, 103.25 mm, 113.02 mm, and 130.92 mm, 
respectively.



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Table 4: Summary of  Goodness of  Fit Statistics and Criteria
Goodness-of-fit statistics Fw Fg Fgum Flgn Fnor
Kolmogorov-Smirnov statistic 0.121 0.086 0.072 0.069 0.118
Cramer-von Mises statistic 0.055 0.021 0.017 0.017 0.042
Anderson-Darling statistic 0.384 0.161 0.133 0.132 0.296
Goodness-of-fit criteria
Akaike's Information Criterion 168.518 165.644 165.115 165.223 167.461
Bayesian Information Criterion 170.407 167.533 167.004 167.112 169.350

Fw=Weibull, Fg=Gamma, Fgum=Gumbel, Flgn=Log-normal, Fnor=Normal

Table 5: Summary of  Disaggregated 24hr Rainfall for different durations (Minute) and Return Period
Frequency (Return Period)
Duration 5-year 10-year 25-year 50-year 100-year
5min 12.90 14.38 15.91 17.42 18.64
10min 18.56 20.70 22.89 25.06 26.81
15min 16.24 18.12 20.04 21.94 23.47
30min 23.33 26.01 28.78 31.50 33.71
60min 29.32 32.70 36.18 39.60 42.37
120min 36.86 41.11 45.47 49.78 53.26
180min 42.14 46.99 51.98 56.91 60.88
360min 52.96 59.07 65.34 71.53 76.53
720min 66.58 74.25 82.14 89.91 96.20
1440min 83.69 93.33 103.25 113.02 120.93

Table 6: Summary of  Disaggregated 24hr Rainfall for different durations (Hour) and Return Period
Duration (Hours) 5-year 10-year 25-year 50-year 100-year
0.083 154.77 172.61 190.95 209.02 223.64
0.17 222.70 248.36 274.75 300.76 321.79
0.25 64.98 72.46 80.16 87.75 93.89
0.5 46.65 52.03 57.56 63.01 67.41

Figure 3: Probability Plot of  Design storm against Return Period based on Log-Normal Distribution

Establishment of  Rainfall Intensity and IDF Curve
Table 5 shows the several lengths of  the 24-hour 
maximum daily design storms broken out. IDF normally 
clarifies the connection among rainfall intensity, rainfall 
length, and return period, thus this was done. It was 

important to break down the design storms into smaller 
periods since most rainfall statistics in Nigeria are linked 
to a cumulative period of  24 hours. Table 5 displays the 
outcome of  disintegrated design storms; while Table 6 
provides the related intensities. 



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1 29.32 32.70 36.18 39.60 42.37
2 18.43 20.55 22.74 24.89 26.63
3 14.05 15.66 17.33 18.97 20.29
6 8.83 9.84 10.89 11.92 12.76
12 5.55 6.19 6.84 7.49 8.02
24 3.49 3.89 4.30 4.71 5.04

Figure 4 shows the existing IDF curve for the project 
area. The established IDF estimates and curves could 
be further applied in hydrologic and hydraulic modeling, 

which are useful for drainage and bridge designs with the 
aim of  reducing the risk of  floods in the project area. 

Figure 4: IDF curves for the catchment system of  the proposed bridge in Kano.

Hydrologic Modeling and Simulations
Table 7 summarizes the watershed parameters used in 
the hydrologic simulation, and Figure 5 represents the 
CN distribution for the basin. Furthermore, Figure 6 
represents the HMS model structures for the project 

region; Figure 7 depicts the hydrograph of  the 100-year 
flood at the proposed bridge; and Table 7 summarizes the 
peak design flood at the proposed bridges, which serves 
as the hydraulic parameter for the bridge designs. 

Table 7: Summary of  Catchment Parameters
Basin Name Length of  the 

longest flow 
path (meters)

Drainage Slope 
(%)

Basin CN Basin Lag 
(Hours)

Basin Slope (%) Basin Area 
(Sq Km)

W200 10028.00 0.007 71.46 2.97 0.039 13.84
W210 17560.86 0.005 69.06 2.39 0.029 5.16
W220 11388.14 0.011 69.51 1.68 0.043 3.51
W230 11313.50 0.011 70.15 1.90 0.042 3.92
W240 10207.44 0.010 71.18 1.36 0.035 3.07
W250 16744.96 0.005 69.57 2.09 0.028 3.29
W260 7896.26 0.011 68.85 0.85 0.034 0.94
W270 8586.94 0.012 71.42 1.65 0.038 2.32
W280 13813.66 0.004 70.76 3.54 0.032 21.56
W290 4738.48 0.010 81.40 0.30 0.021 0.02
W300 12278.30 0.006 71.45 3.11 0.032 10.67
W310 6098.62 0.010 71.90 1.66 0.040 4.38
W320 5987.53 0.008 71.42 1.69 0.038 2.67
W330 2042.46 0.008 78.09 0.35 0.028 0.03
W340 2929.23 0.009 73.96 0.93 0.034 0.61
W350 3427.75 0.008 70.27 1.21 0.035 1.55



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W360 3944.18 0.007 70.70 1.83 0.031 2.22
W370 6843.01 0.008 69.37 1.90 0.034 2.70
W380 6988.57 0.008 67.24 2.16 0.031 3.22

Figure 5: Curve Number (CN) for the Catchment Areas of  the Proposed Bridge

Figure 6: Hydrologic Model of  Flood Discharged at the Proposed Bridge



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Figure 7: Hydrologic Model of  Flood Discharged at the Proposed Bridge

CONCLUSION 
Along with the appropriate IDF curves for the same 
return duration, this study produced rainfall depths for 
several return periods: five years, ten years, twenty five 
years, fifty years and one hundred years. The simulation 
of  the peak flow of  every catchment with an outlet 
suggested bridge location was driven by the known IDF 
estimations, catchment characteristics, and CN. Based 
on the gathered data, this study finds that the design 
floods are relevant for the construction of  bridges in 
Kano  State, Nigeria. Furthermore, the results obtained 
fit the numbers reported by Ahmed et al. (2021) in an 
earlier study conducted to determine the rainfall intensity, 
rainfall duration, and return period in Abuja, Nigeria, 
utilizing a dataset spanning 35 years.

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