Rainfall intensity is considered one of the basic factors in designing hydrological models based on rainstorm data. The objective of this research is to employ novel intensity–duration–frequency curves and develop empirical equations for rainfall intensity in the city of Kirkuk. The reduction formula adopted by the Indian Meteorological Department was used to divide the maximum daily rainfall for short periods of 0.5, 1, 2, 4, 6, 12, and 24 h. Three key methods of frequency analysis (lognormal distribution, log Pearson type III distribution, and Gumbel extreme value distribution) were utilized to formulate a statistical relationship based on rainfall intensity data from between the years 1981 and 2023 for a gauging station upstream of the Kirkuk city basin to provide the best data set for all periods of 100, 50, 25, 10, 5, and 2 years. Research has shown that the logarithmic distribution is the best fit for modelling the relationship between the annual maximum rainfall at Kirkuk station and duration of the rainfall. The goodness-of-fit results indicate that the lognormal distribution statistically outperforms other distribution models. Hence, the generated rainfall intensity, duration, and frequency curves that were developed led to estimating the intensity of precipitation to build forecasting and hydrological behaviour of the Kirkuk city basin.

  • The paper created rainfall intensity–duration–frequency (IDF) curves using statistical distribution tests adapted to Kirkuk city, Iraq.

  • Historical rainfall data were analysed.

  • The generated IDF curves were compared to current methodologies or standards.

  • The IDF curves for Kirkuk city's rainfall durations and return periods were derived from the statistical analysis.

  • Data constraints or model selection uncertainties were identified and advice for future research is presented.

It is important to have a good idea of both the infrastructure's intended purpose and the physical conditions in which it will work. The rainfall intensity–duration–frequency (IDF) curves are used in several hydrological studies of hydraulic facilities and infrastructure that require safe hydraulic design. The IDF curve establishes a relationship between the rainfall intensity, duration, and frequency at which it occurs (Tuama Al-Awadi & Affairs 2016; Ewea et al. 2018). Thus, in the process of the management of stormwater, the design criteria of infrastructure system components are applied to the events of rainfall to the heavy return period (Mohammed et al. 2021). The data are typically presented as IDF curves that are obtained from analysis of the statistics regarding events that are highly unusual or exceptional based on the intended objective of the application; it can be generated employing various time intervals ranging from immediate daily maximum intensity to annual, monthly, and weekly intensities (Nyamathi & Yashas Kumar (2021)).

Different studies indicate the use of different methodologies to develop IDF curves for different regions worldwide. Table 1 summarizes these studies' most important findings and methods.

Table 1

A literature review on rainfall intensity–duration–frequency (IDF) interval curves

ReferenceLocationMethod/ApproachKey findings
Ewea et al. (2018)  Saudi Arabia Gumbel type-I distribution Developed empirical equations for rainfall intensity 
Tuama Al-Awadi & Affairs (2016)  Baghdad, Iraq Log Pearson type III distribution Established the relationship between rainfall intensity, duration, and frequency 
Mohammed et al. (2021)  Nigeria Lognormal probability distribution Suggested using IDF curves for designing infrastructure systems 
Nyamathi & Yashas Kumar (2021)  India Gumbel's extreme value distribution Presented IDF curves obtained from statistical analysis 
Qarani Aziz et al. (2023)  North Iraq Gumbel method Developed empirical rainfall intensity equations for each station 
Hussein et al. (2023)  North Iraq (Mosul) Log Pearson type III distribution Found log Pearson type III suitable; rainfall intensity increases with return periods and decreases with duration 
Mahdi & Mohamedmeki (2020)  Baghdad, Iraq Gumbel, log Pearson type III, lognormal Found no significant difference among methods; log Pearson type III is slightly preferred 
Hussein (2014)  Karbala, Kut, Iraq Log Pearson type III distribution Found log Pearson type III to be the best fit 
Zeri et al. (2023)  Major cities in Iraq Global Satellite Mapping of Precipitation (GSMaP GC) Developed IDF curves using satellite data 
Sun et al. (2019)  Singapore GSMaP GC Improved reliability and accuracy of IDF curves, especially for short durations 
Ashok Kumar et al. (2023)  India Gumbel distribution, empirical reduction method Found IDF curves useful for deriving design storms 
AlHassoun (2011)  Riyadh, Saudi Arabia Gumbel, log Pearson type III, lognormal Developed an empirical formula for estimating design rainfall intensity 
Odiong & Agunwamba (2023)  Nigeria Non-stationary rainfall model Developed a high-accuracy model and compared it with other models for calibration and validation 
Anand et al. (2023)  India Tool development Developed a tool for engineers to calculate rainfall IDF curves 
Onen & Bagatur (2017)  Saudi Arabia Simplified Gumbel's method Estimated flood discharge using gene expression programming and regression analysis models 
Akpen et al. (2019)  Lokoja, Nigeria Log Pearson type III distribution Recommended using IDF curves for designing hydraulic structures 
Hidayati et al. (2023)  Pontianak City, Indonesia Log Pearson type III distribution Derived IDF curve using rainfall data from four stations 
ReferenceLocationMethod/ApproachKey findings
Ewea et al. (2018)  Saudi Arabia Gumbel type-I distribution Developed empirical equations for rainfall intensity 
Tuama Al-Awadi & Affairs (2016)  Baghdad, Iraq Log Pearson type III distribution Established the relationship between rainfall intensity, duration, and frequency 
Mohammed et al. (2021)  Nigeria Lognormal probability distribution Suggested using IDF curves for designing infrastructure systems 
Nyamathi & Yashas Kumar (2021)  India Gumbel's extreme value distribution Presented IDF curves obtained from statistical analysis 
Qarani Aziz et al. (2023)  North Iraq Gumbel method Developed empirical rainfall intensity equations for each station 
Hussein et al. (2023)  North Iraq (Mosul) Log Pearson type III distribution Found log Pearson type III suitable; rainfall intensity increases with return periods and decreases with duration 
Mahdi & Mohamedmeki (2020)  Baghdad, Iraq Gumbel, log Pearson type III, lognormal Found no significant difference among methods; log Pearson type III is slightly preferred 
Hussein (2014)  Karbala, Kut, Iraq Log Pearson type III distribution Found log Pearson type III to be the best fit 
Zeri et al. (2023)  Major cities in Iraq Global Satellite Mapping of Precipitation (GSMaP GC) Developed IDF curves using satellite data 
Sun et al. (2019)  Singapore GSMaP GC Improved reliability and accuracy of IDF curves, especially for short durations 
Ashok Kumar et al. (2023)  India Gumbel distribution, empirical reduction method Found IDF curves useful for deriving design storms 
AlHassoun (2011)  Riyadh, Saudi Arabia Gumbel, log Pearson type III, lognormal Developed an empirical formula for estimating design rainfall intensity 
Odiong & Agunwamba (2023)  Nigeria Non-stationary rainfall model Developed a high-accuracy model and compared it with other models for calibration and validation 
Anand et al. (2023)  India Tool development Developed a tool for engineers to calculate rainfall IDF curves 
Onen & Bagatur (2017)  Saudi Arabia Simplified Gumbel's method Estimated flood discharge using gene expression programming and regression analysis models 
Akpen et al. (2019)  Lokoja, Nigeria Log Pearson type III distribution Recommended using IDF curves for designing hydraulic structures 
Hidayati et al. (2023)  Pontianak City, Indonesia Log Pearson type III distribution Derived IDF curve using rainfall data from four stations 

The main objective of this work is to formulate IDF curves for Kirkuk city for varying return periods, where three different methods of statistical distributions are utilized to achieve the objectives. The software EasyFit 5.6 is applied to verify the probability distribution function for the data of the maximum daily precipitation. These curves and equations are very important for enhancing hydrological analysis that can be used for the safe and economical design of hydraulic components represented by designing systems of drainage in urban areas, such as storm sewers, canals, and any required hydraulic structures in the city of Kirkuk.

The study area is the city of Kirkuk in the Kirkuk governorate, in northeastern Iraq, to the north of the capital Baghdad. The Khassa Chai River runs through the Kirkuk city with its watershed at a latitude of 35°28′42.8340″ N and a longitude of 44°24′6.9552″ E. Figure 1 represents the total area of the Kirkuk city watershed, which is 872 km2. The city's topography is approximately flat; the Kirkuk city watershed basin varies from flat to Tarren (Mahmoud & Kasim 2019). Kirkuk city has approximately 1,100,000 people and an annual growth rate of 2.33%.
Figure 1

Study area (Kirkuk city within Khassa Chai basin).

Figure 1

Study area (Kirkuk city within Khassa Chai basin).

Close modal
The Meteorological Station of Kirkuk provides climate data assembled by the Iraqi Meteorological Organization (IMO). Table 2 shows a summary of climatic elements covered (Najdat 2015). Daily precipitation data from 1981 to 2023 is modified with calibration from the available satellite's daily precipitation data and Kirkuk station for missing or unknown data (Kidd & Huffman 2011; Aboelkhair et al. 2019). Figure 2 shows a disaggregation of maximum and minimum daily precipitation data.
Table 2

Climatic elements (Najdat 2015)

Climatic elementMaximumMinimumAverage
Precipitation (mm/month) 768.9 202.5 368.4 
Relative humidity (%) 73 23 47 
Evaporation (mm) 387.9 45.6 … 
Wind speed (m/s) 28 … 2.9 
Evaporation in free water surface/year (mm) … … 1,642.9 
Temperature (°C) 49.53 −6.7 22.4 
Climatic elementMaximumMinimumAverage
Precipitation (mm/month) 768.9 202.5 368.4 
Relative humidity (%) 73 23 47 
Evaporation (mm) 387.9 45.6 … 
Wind speed (m/s) 28 … 2.9 
Evaporation in free water surface/year (mm) … … 1,642.9 
Temperature (°C) 49.53 −6.7 22.4 
Figure 2

Disaggregation of maximum and minimum daily precipitation data.

Figure 2

Disaggregation of maximum and minimum daily precipitation data.

Close modal
The climate data for precipitation included the value of maximum daily precipitation from 1981 to 2023, which is segmented into small intervals of half hour and noted as 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 6, 12, and 24 h. Values of the empirical equation were estimated depending on Equation (1) for reduction, which was prepared by the Indian Metrological Department (IMD):
(1)
where is the precipitation depth required at the interval of time hour (t-hour), P(24) is the precipitation quantity in the day, and is the duration of the rainfall in hours of the required precipitation depth. Figure 3 shows the distribution of the required precipitation depth (in mm) for t-hour duration generated from daily maximum precipitation across the year.
Figure 3

The distribution of rainfall depths derived from maximum annual values for various durations throughout the year.

Figure 3

The distribution of rainfall depths derived from maximum annual values for various durations throughout the year.

Close modal

An established method to understand the relationship between precipitation and storm frequency is the IDF curve. It is generally adopted to demonstrate the design of storms for different systems of water projects of certain recurrence intervals (AlHassoun 2011). It is important to understand that IDF curves are not generated from specific storm events and as such do not represent the probability of a particular storm's occurrence. The initial phase in developing the IDF curves is to fit various distributions of the frequency of theoretical amounts to the extreme rainfall for some fixed intervals.

The next logical phase is to proceed and then describe the variation of the parameters of the distribution with intervals by a functional relation. Then any duration and return period can be generated and formulated from the fitted relationships of rainfall intensity. In this study, the values of availability to the maximum annual of the intervals are statistically analysed by using three methods of distribution keys (Gumbel extreme value, lognormal, and log Pearson type III). The optimal fit was identified using EasyFit 5.6 software.

  • Rainfall intensity (I)

The rainfall intensity obtained by the rainfall data is divided by an interval as follows:
(2)
where P is the precipitation (mm), t is the duration (h), and I is the intensity (mm/h).
  • Standard deviation, mean, and skewness coefficient

The following formulas were used to find the mean (), standard deviation (S), and skewness coefficient (Cs) for all the chosen intervals (Akpen et al. 2019):
(3)
(4)
(5)
  • Frequency factor

For each of the return periods that were chosen, the frequency factor calculation using the chosen distributions is now complete. Gumbel, lognormal, and log Pearson type III distributions were utilized in this investigation. Table 3 describes the frequency factors for various distributions.

Table 3

The factors of frequency for the different distributions

N/SDistributionFrequency
Gumbel generalized extreme distribution value type-I  
Lognormal In the case of a normal distribution, the only difference is the variables of the logarithm to be used, i.e.,  
Log Pearson type III With G = 0, a factor of frequency is equal to Z of the standardization of the normal variable. With KT, G is roughly by Chow et al. (1988) as KT = (z) + [(z 2–1) k] + [1/3*(z 3–6*z) * k2] – [(z2 – 1)*k] + (2*k4 + 1/3* k5) where the value of k = [G/6]. The value of KT can be obtained from the table of standardization statistics 
N/SDistributionFrequency
Gumbel generalized extreme distribution value type-I  
Lognormal In the case of a normal distribution, the only difference is the variables of the logarithm to be used, i.e.,  
Log Pearson type III With G = 0, a factor of frequency is equal to Z of the standardization of the normal variable. With KT, G is roughly by Chow et al. (1988) as KT = (z) + [(z 2–1) k] + [1/3*(z 3–6*z) * k2] – [(z2 – 1)*k] + (2*k4 + 1/3* k5) where the value of k = [G/6]. The value of KT can be obtained from the table of standardization statistics 

Gumbel method

The Gumbel distribution method (the generalized extreme value distribution type-I) is a probability and statistics theory used to model the highest or lowest values from different distributions of a set of samples (Chow et al. 1988; McCuen 1997; Hirsch et al. 2022). Equation (6) can help to estimate the frequency of precipitation PT in mm for a given interval and return period TR in years (Onen & Bagatur 2017; Shamkhi et al. 2022):
(6)
where PT is the frequency of rainfall in mm for each interval, S is the standard deviation for the data of precipitation, Pave. is the data of average annual precipitation, and listed in Table 2, KT is the frequency factor of the Gumbel extreme value:
(7)
where TR represents the return period for 2, 5, 10, 25, 50, and 100 years. Then, the intensity of rainfall IT in mm/h for the return period TR in years is calculated using the following equation:
(8)
where Td is the time duration (h).

Log Pearson type III

To predict the potential floods of a stream in a particular place, log Pearson type III distribution is utilized as a statistical method that could be applied to fit the frequency distribution data (Chow et al. 1988). The advantage of this method is its ability to make projections for flood events that have return periods far beyond the recorded events of floods (McCuen 1997). The distribution expression is given by Equation (9):
(9)
where P*ave. indicates the value of average to the P* where taking the logarithm for precipitation value, S* represents the logarithm values of standard deviation, and KT is the factor frequency of Pearson, which depends on the period TR and skewness coefficient G (Shamkhi et al. 2022). The factor values KT could be sourced from references in many tables (Chow et al. 1988). The parameter of skewness G is calculated as follows:
(10)
where N indicates the sample size in recorded years.

Lognormal method

The lognormal way works through the parallel procedure as log Pearson type III, used in Gumbel's method with normal KT (Shamkhi et al. 2022).

Fitting of a probability distribution

In this study, the Gumbel extreme value, lognormal, and log Pearson type III were considered for every data series of intervals. The software EasyFit 5.6 is utilized for fitting the distribution probabilities for the variety of intervals of precipitation information. To evaluate the suitability of each distribution of probability, several statistical procedures are used, including the least summation of statistical modelling identify criteria (LSSMIC), the graph of cumulative distribution function (CDF), the test of goodness of fit, and the graph of probability density function (PDF), as presented in Figure 4.
Figure 4

Evaluating process for suitability of probability distribution through statistical tools.

Figure 4

Evaluating process for suitability of probability distribution through statistical tools.

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Descriptive statistics for duration series

The statistic parameters of the interval's series of rainfall for 24 h indicated that the means of the rainfall sample for 43 years of data in 24 h are 56.69 mm, and the standard deviation is 17.95 mm. The sample coefficient of variation and skewness is 0.32 and 0.70, respectively, the excess kurtosis is 0.0043, and the variance is 322.37. The statistics descriptive of 0.5, 1, 4, 6, 12, and 24 h are presented in Table 4.

Table 4

The statistics of descriptive intervals series

Statistic0.5 h1 h4 h6 h12 h24 h
Size of the sample 43 43 43 43 43 43 
Range 19.71 24.84 39.43 45.13 56.86 71.64 
Mean 15.60 19.65 31.20 35.71 45.00 56.69 
Variance 24.41 38.74 97.63 127.93 203.08 322.37 
Standard deviation 4.94 6.22 9.88 11.31 14.25 17.95 
Coefficient of variation 0.32 0.32 0.32 0.32 0.32 0.32 
Standard error 0.75 0.95 1.51 1.72 2.17 2.74 
Skewness 0.70 0.70 0.70 0.70 0.70 0.70 
Excess kurtosis 0.0043 0.0043 0.0043 0.0043 0.0043 0.0043 
Statistic0.5 h1 h4 h6 h12 h24 h
Size of the sample 43 43 43 43 43 43 
Range 19.71 24.84 39.43 45.13 56.86 71.64 
Mean 15.60 19.65 31.20 35.71 45.00 56.69 
Variance 24.41 38.74 97.63 127.93 203.08 322.37 
Standard deviation 4.94 6.22 9.88 11.31 14.25 17.95 
Coefficient of variation 0.32 0.32 0.32 0.32 0.32 0.32 
Standard error 0.75 0.95 1.51 1.72 2.17 2.74 
Skewness 0.70 0.70 0.70 0.70 0.70 0.70 
Excess kurtosis 0.0043 0.0043 0.0043 0.0043 0.0043 0.0043 

From Table 4, it can be observed that all data durations have a skewness value of approximately 0.70. This indicates that the duration or interval of data is distributed symmetrically. Moreover, extra kurtosis of the entire duration of data is uniform equal to 0.0043, meaning that the distribution of each data interval does not exhibit substantial divergence from a normal distribution. Table 4 presents the statistical descriptors of the EasyFit 5.6 software to get the finding of interval series.

Graphical determination of the best modelling to 0.5 h

The graph of PDF presented in Figure 5 shows that all tested distributions fit the data well, according to the graphical identification. As clarified in Figure 5, the LSSMIC and goodness-of-fit test provide the distribution data as the best fitting. All distribution frequency curves (Gumbel, log Pearson type III, and lognormal) have a single peak that classifies them as approximately symmetrical and unimodal. This is in line with the statistical description obtained in Table 3 for the skewness statistics results. The graph of CDF shown in Figure 6 demonstrates that observed rainfall will not exceed the magnitude regarding non-exceedance probability.
Figure 5

PDF distributions for the selected 0.5 h.

Figure 5

PDF distributions for the selected 0.5 h.

Close modal
Figure 6

CDF distributions for the selected 0.5 h.

Figure 6

CDF distributions for the selected 0.5 h.

Close modal

Goodness-of-fit tests

The goodness-of-fit tests display the probability distributions that have been obtained, with the least statistic value being considered the most suitable fitting distribution. Table 4 clears the statistical results of the Kolmogorov–Smirnov, Anderson–Darling, and Chi-square tests of goodness of fit for 0.5 h durations. From Table 5, the lognormal and log Pearson distributions are commonly found to be the most suitable fit. Applying the Chi-square test, the 6th ranked was at lognormal distribution by Kolmogorov–Smirnov and Anderson–Darling goodness-of-fit tests. The 12th ranked was at log Pearson type III by the test of Kolmogorov–Smirnov, 2nd by the test of Anderson–Darling, and 3rd by the test of Chi-square. The 5th ranked was at Gumbel distribution by the test of Kolmogorov–Smirnov, 21st by the test of Anderson–Darling, and 17th by the test of Chi-square.

Table 5

Tests of fit for 0.5h

DistributionKolmogorov–Smirnov
Anderson–Darling
Chi-square
StatisticRankStatisticRankStatisticRank
Gumbel 0.0918 5th 0.4388 21st 0.5850 17th 
Lognormal 0.0919 6th 0.3930 6th 0.2494 4th 
Log Pearson type III 0.0961 12th 0.3808 2nd 0.2359 3rd 
DistributionKolmogorov–Smirnov
Anderson–Darling
Chi-square
StatisticRankStatisticRankStatisticRank
Gumbel 0.0918 5th 0.4388 21st 0.5850 17th 
Lognormal 0.0919 6th 0.3930 6th 0.2494 4th 
Log Pearson type III 0.0961 12th 0.3808 2nd 0.2359 3rd 

Least sum of statistic model identification criterion

From Table 5, the goodness-of-fit test shows that Gumbel, lognormal, and log Pearson type III distributions are close in the value of statistics, where the best fit is adopted according to the lowest statistic value. However, the goal is to obtain the best fitting curve, which is achieved and integrated with the LSSMIC:
(11)

Table 6 displays the most suitable model among the three distributions of probability that were taken into account. It is evident from Table 5 that the lognormal distribution has the smallest statistical value of 0.03366, and the Gumbel distribution has a value of 0.11566. In cases where the logarithmic distribution best fits the relationship between the annual maximum rainfall at Kirkuk station and a 0.5-h duration, it is employed for subsequent analyses. Likewise, rainfall data with durations of 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 6, 12, and 24 h were fitted with a probability distribution.

Table 6

The model of best fit for 0.5h

DistributionKolmogorov–SmirnovAnderson–DarlingChi-squareLSSMICFit
statisticstatisticstatistic
Gumbel extreme value 0.09188 0.43883 0.58495 0.11566  
Lognormal 0.09188 0.39239 0.54939 0.03366 Best 
Log Pearson type III 0.09611 0.38004 0.23587 0.28798  
DistributionKolmogorov–SmirnovAnderson–DarlingChi-squareLSSMICFit
statisticstatisticstatistic
Gumbel extreme value 0.09188 0.43883 0.58495 0.11566  
Lognormal 0.09188 0.39239 0.54939 0.03366 Best 
Log Pearson type III 0.09611 0.38004 0.23587 0.28798  

Standard deviation and mean to the intensity of rainfall

Table 7 shows the finding of the standard deviation and mean obtained from each duration series, according to Equations (2) and (3) for computing the standard deviation and the mean for each data duration of rainfall intensities.

Table 7

The rainfall intensity standard deviation and mean for all durations

Duration0.5 h1 h1.5 h2 h4 h12 h24 h
Mean 15.60 19.65 22.50 24.76 31.20 45.00 56.69 
Standard deviation 4.94 6.22 7.13 7.84 9.88 14.25 17.95 
Duration0.5 h1 h1.5 h2 h4 h12 h24 h
Mean 15.60 19.65 22.50 24.76 31.20 45.00 56.69 
Standard deviation 4.94 6.22 7.13 7.84 9.88 14.25 17.95 

Developing IDF curves through the generated intensity of rainfall design

The intensity of rainfall design was derived using Equation (12), and the findings are represented graphically. By Mohammed et al. (2021), the amount of the event hydrologically [XT] could be described as follows:
(12)
where XT is the size of the event hydrologically, represents the mean value, KT is the frequency factor, and S represents the standard deviation. Figures 7 and 8 represent the relation between rainfall intensity for a given return period and the duration revealing that the intensity of rainfall is proportional directly to the return period and proportional inversely to the duration of rainfall. It should be noted that when the duration of rainfall increases, the intensity of rainfall decreases for a particular return period. For a given duration of rainfall, the intensity of rainfall rose as the return period grew. Furthermore, it should be noted that for a particular return period, there is a drop in rainfall intensities as the duration of rainfall increases. Therefore, it can be asserted that minor quantities of discharge will result from rainfall of sufficient duration and low intensity. Simultaneously, when there is a high intensity of rainfall in a short period, it results in substantial surface runoff. Hence, it is imperative to consider the long return periods when designing major hydraulic infrastructure like bridges and dams for safety and cost-effectiveness. Conversely, the design of minor hydraulic infrastructure such as systems of drainage and culverts should take into account shorter return periods (AlHassoun 2011; Ewea et al. 2018; Mohammed et al. 2021; Ashok Kumar et al. 2023).
Figure 7

IDF curves.

Figure 8

IDF log-scale curves.

Figure 8

IDF log-scale curves.

Close modal
According to the hypothetical model generated from previous equations, tables and figures were used to develop the IDF curves, where the intensity I of rainfall decreases exponentially with the duration D. The general form of the IDF Equation (12) for each return period T can be given by:
(13)
where a(T) and b(T) are coefficients that depend on return periods T, and D is the interval in hours. The coefficients were chosen arbitrarily to illustrate the shape of typical IDF curves.

The developed IDF curves for Kirkuk city should be applied for calibration and verification processes according to the observed actual data using hydrological modelling, especially in geospatially and kinetic routing-based models, to determine the general hydrological behaviour of watersheds that impact the infrastructure of Kirkuk city. Then, the developed IDF curve can be utilized in the design data for different infrastructure systems (such as drainage systems, and in management of urban water systems such as bridges, sewers, and culverts). Due to variability patterns of rainfall data and climate change, the developed IDF curve must be applied to the review and for updating because of the lack of data and long-term observed data; in addition, the city of Kirkuk classified most of its watersheds as ungagged watersheds owing to the fact that its basins are not measured. Research has shown the logarithmic distribution is the best fit for modelling the relationship between the annual maximum rainfall at the Kirkuk station and its duration. The goodness-of-fit results indicate that the lognormal distribution statistically outperforms other distribution models. Additionally, the rainfall intensity increases as return periods increase but decreases as rainfall duration increases. Hence, the generated rainfall intensity, duration, and frequency curves that were developed led to estimating the intensity of precipitation to build forecasting and hydrological behaviour of the Kirkuk city basin.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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