Introduction:
Floods are among the natural disasters that pose a serious threat to lives and property. Flood frequency analysis is essential for estimating design discharges for hydraulic structures and managing flood risk. Two primary methods for estimating design floods include statistical and hydrological approaches. Statistical methods typically use probability distribution functions such as Gumbel, log-normal, and Pearson Type III to analyze peak discharges. In areas with insufficient recorded data, rainfall data and regional analyses are utilized. Low-probability events and sparse historical data significantly impact analysis results. These data may lead to deviations in discharge estimations and alter return period assessments. Various statistical methods have been introduced for identifying and removing outliers; however, incorporating historical data can enhance modeling accuracy. Studies have shown that including historical data in statistical analyses improves the precision of design flood estimates. This study aims to examine outlier data at the Takht Khan hydrometric station, located in the Godarkhosh River Basin, Ilam, and analyze the impact of removing or retaining these data on the accuracy of discharge estimates for different return periods.
 Methods:
This study investigates flood estimation in the Godarkhosh River watershed in Ilam Province, Iran, using statistical and hydrological analysis methods. The watershed, covering approximately 810 km², consists of mountainous terrain with seasonal river discharge variations. Key meteorological and hydrometric data were collected, including 34 years of rainfall and discharge records. Outlier detection is crucial in hydrological studies as extreme values can significantly impact statistical analyses and flood prediction accuracy. This study employed three methods for identifying outliers: graphical methods (box plots and scatter plots), statistical methods (Z-score analysis), and model-based methods (cluster analysis).The box plot method visualizes data dispersion and identifies extreme values, while scatter plots reveal potential anomalies in variable relationships. The Z-score method standardizes data by measuring deviations from the mean, with values exceeding ±3 considered outliers. Cluster analysis groups similar data points and detects anomalies based on deviations from main clusters. For flood frequency analysis across different return periods, the Log-Pearson Type III distribution was selected for discharge modeling based on the goodness-of-fit tests, including the Anderson–Darling and Chi-square tests. Given the natural skewness of flood data, this distribution provides more reliable estimates of peak discharge for various return periods. The method involves logarithmic transformation of the data, calculation of the mean, standard deviation, and skewness coefficient, followed by fitting the Pearson Type III distribution. Accurate flood estimation is essential for the design of hydraulic structures and effective flood risk management. Identifying and appropriately handling outlier data improves data quality and enhances the reliability of hydrological modeling. The findings of this study highlight the importance of simultaneously using multiple outlier detection techniques to improve statistical analyses and increase the accuracy of flood prediction in watersheds prone to extreme hydrological events.
 Results:
Descriptive analysis of the hydrological data for the Godarkhush River indicated that for two key variables of annual maximum discharge and annual maximum precipitation, the skewness and kurtosis values were 3.87 and 17.53 for discharge, and 2.11 and 5.01 for precipitation, respectively. These values reflect a distribution with notable positive skewness and high kurtosis, commonly indicative of the presence of outliers in the dataset. Outliers can significantly affect statistical analyses and hydrological modeling; thus, their identification is crucial. To detect outliers, multiple methods were employed, including Box Plot, Z-Score method, and Cluster Analysis. The results consistently identified the discharge data for the year 2015, with a value of 2,160 m³/s, as an outlier across all methods. Subsequently, to determine the most suitable probability distribution for modeling annual maximum discharges, four common distributions (Log-Pearson Type III, Log-Normal, Weibull, and Gumbel Max) were evaluated using the EasyFit statistical software. According to the Anderson–Darling test, which is particularly sensitive to deviations in the tails of the distribution, the Log-Pearson Type III distribution yielded the lowest statistic (0.341), indicating the best fit. Similarly, based on the Chi-Squared test, this distribution also showed the best agreement with the observed data. Therefore, Log-Pearson Type III was selected as the most appropriate distribution for modeling annual peak discharge data in this study. To estimate design discharge values using the Log-Pearson Type III distribution, key distribution parameters (mean, standard deviation, and skewness) were calculated for the Takht-e-Khan hydrometric station under both conditions of with and without the identified outlier. The results showed that the inclusion of the outlier increased the mean annual discharge from 231.87 to 288.59 m³/s, highlighting the significant impact of extreme flood events on computed values. The skewness also increased by 1.77 units when the outlier was included. Moreover, kurtosis rose from 4.29 to 17.53 under the same condition, suggesting that including rare extreme events can considerably alter design flow estimations. Following this, design discharge values were calculated using the Log-Pearson Type III distribution for various return periods (5 to 1000 years), both with and without the outlier. The results revealed that for short return periods, the differences in design discharge between the two scenarios were minimal. However, for medium-term return periods (25 to 100 years), the disparity increased with the return period. For instance, at a 50-year return period, the design discharge was estimated at 1,481.5 m³/s with the outlier and 894.15 m³/s without it that indicated a 39.64% reduction when the outlier was excluded. Similarly, in long-term return periods (200 to 1000 years), the differences became even more pronounced. For the 1000-year return period, the design discharge was calculated at 7,152.4 m³/s with the outlier, and 2,532.9 m³/s without it, reflecting a 64.58% decrease that demonstrated the substantial influence of outlier events on long-term hydrological estimates.
 Conclusion:
The findings of the study emphasize that managing outlier data and making the correct decision about including or excluding it from datasets, especially in flood analysis and design discharge estimation, can significantly affect the accuracy of predictions and hydrological designs. Based on the results, the flood discharge data for the year 2015 (2160 m³/s) was identified as an outlier. Due to its significant deviation from other data, this outlier can cause major changes in the design discharge estimates. Excluding this data from the dataset leads to a considerable reduction in the design discharge for long return periods, which could result in underestimating the risk of severe floods. Moreover, including the discharge data in 2015, as an exceptional data point, in the calculations improves the accuracy of predictions and the design of hydrological structures. These results highlight the importance of proper management of outlier data and the correct decision-making process regarding its inclusion or exclusion in order to avoid significant errors in predictions and designs.