A rainfall intensity (Depth), duration, frequency (IDF or DDF) relationship is needed for planning of water resources projects. The frequencies of high-intensity rainfalls is required for several engineering purpose, one of the most important is the estimation of extreme floods for inadequately gauged basins. In general, rainfall is associated with the floods of sub catchment or small catchment of shorter duration, similarly where the stream size decrease, their chances of being adequately gauged also decrease, and so it may be argued that short – duration rainfalls of less than 2 or 3 hr are of special importance in flood estimation. In this study the analysis of DDF for Iran has been carried out using synoptic meteorological stations and depth - duration ratio of shorter durations (15 minutes to 12 hr) to maximum 24hr (Rt/24) in all existing station. By using these values, isolation maps were plotted and than the median values of Rt/24 were selected for any climatic regions. The DDF relationship of rainfall for any climatic regions of Iran obtained by regression method based on duration and Rt/24.

Introduction One of the important consequences of climate change is a change in the frequency and intensity of rainfall. In fact, it can be said that as a result of this phenomenon (climate change), in many parts of the world, the frequency and intensity of maximum rainfall have increased. However, the type and severity of these changes vary from region to region (IPCC, 2012: 5). In recent decades, in the framework of climate change, several studies have been conducted on the trend of rainfall in most parts of the world. Most of these studies are based on parametric or non-parametric methods such as linear regression analysis, Spearman's test, age gradient test, and Mann-Kendall test. However, the use of these methods requires some limiting assumptions. In addition, these tests only show the trend of changes in the average time series, while they do not provide any information about the trend of changes in different time series classes. In this regard, Sen (2012: 1044) proposed the ITA method, which addresses the above-mentioned problems in addition to allowing a trend to be identified in a series of "low", "medium" and "high" values. Materials and methods In this study, in order to achieve the defined goal, the basic method of percentiles was initially used. Since the choice of the threshold value of the base percentile is a matter of taste and does not reflect the intensity-frequency of heavy rainfall, the type 1 equation probabilistic distribution function (Gamble) was used to determine the heavy precipitation threshold to provide a criterion that results in intensity-frequency of occurrence, while it is based on time series distribution of the precipitation data. For this purpose, first the data of rainy days related to 6 synoptic stations in the west of the country from 1961-2019 were obtained from the Meteorological Organization. Then, in order to calculate the maximum amount of daily rainfall during different return periods, the Gamble distribution function was used, based on which the heavy rainfall threshold was defined for the stations in the region and the maximum daily rainfall values during the return periods of 2, 5, 10, 15, 20, 25, 50 and 100 years were calculated. Finally, MK and ITA tests were used to determine the trend of these precipitations. The ITA method was proposed by Sen. Despite its simplicity, it does not require any presuppositions and is more capable than other non-parametric methods because this method is able to identify hidden trends and internal trends in time series in addition to uniform trends. Therefore, in this study, ITA method was used to identify the uniform and non-uniform trends in the maximum daily rainfall and the total annual rainfall in the west of the country. Research Findings After determining the thresholds of heavy rainfall using the Gamble distribution function, it became clear that the average rainfall of more than 37 mm in the western region of the country is considered heavy rainfall. The heavy rainfall index of Dezful station was higher than other stations, which indicates the high intensity of daily rainfall in this station. In this study, heavy precipitation threshold was calculated for all stations by applying the percentile method on rainy days with a minimum threshold of 1 mm. Then, ITA method was used to analyze the trend and determine the behavior of total annual rainfall and maximum daily rainfall in the study area. Application of this method on the total annual rainfall of Khorramabad station showed that middle floor precipitation (430-650) of this station is decreasing, while upper and lower floor precipitation was decreasing. In Hamedan station, the precipitation of the middle class (240-240) showed a significant decreasing trend, but no significant trend was observed in the lower class (less than 240) and the upper class (above 440). In Kermanshah, Dezful, Ahvaz and Abadan stations, the trend specified in all classes was decreasing and uniform. The application of Man-Kendall method on the total annual rainfall in the study area showed that the trend of these rains is decreasing in all stations and is significant in Khorramabad, Hamedan, Kermanshah and Dezful at the level of 95%. Regarding the application of ITA method for maximum daily rainfall of Gamble, the results showed that in Khorramabad station, rainfall with a return period of 5, 10, 15, 20 and 25 years of this station increased and precipitation with a return period of 2 years showed no particular trends. At Abadan station, rainfall with a return period of 50 years showed a decreasing trend. In Dezful and Ahvaz stations, the trend marked in all classes was a decreasing trend. In general, no specific trend was observed in Hamedan and Kermanshah stations. Regarding the maximum daily rainfall of Gamble, the results of Mk showed a negative trend in Hamedan, Kermanshah, Ahvaz and Abadan stations and a positive trend in Khorramabad and Hamedan, but only in Ahvaz station, the trend was significant at 95%. In the present study, some conflicting results have been obtained by comparing the ITA and MK methods. This shows the advantage of this method over other process tests. For example, while the Mann-Kendall test on Khorramabad station showed a significant decrease in the total annual rainfall of this station, the Sen method showed a different trend from this method. In fact, according to ITA, it was found that the total rainfall in Khorramabad had an uneven trend, which was divided into three classes, and the precipitation class showed 430 to 650 decreasing trends less than 430 and more than 650 increasing trends in this station. Result The results of ITA method showed that on an annual scale, there is a non-uniform trend in rainfall in Khorramabad and Hamedan. But in Kermanshah, Dezful, Ahvaz and Abadan stations, the trend marked in all classes was decreasing and uniform. On a daily scale, the results showed that precipitation with a return period of 5, 10, 15, 20 and 25 years of this station is an increasing trend and precipitation with a return period of 2 years is without a trend. At Abadan station, rainfall with a return period of 50 years showed a decreasing trend. In Dezful and Ahvaz stations, the trend marked in all classes was a decreasing trend. In Hamedan and Kermanshah stations, in general, no specific trend was observed, but in more detail, it can be said that the trend of rainfall on the upper floor of Hamedan station was increasing, whereas the trend was decreasing in Kermanshah station. The results of Mann-Kendall test also showed that on an annual scale, all stations have a decreasing trend and on a daily scale, Hamedan, Kermanshah, Ahvaz and Abadan stations have a negative trend, although Khorramabad and Hamedan stations showed a positive trend in precipitation. In fact, when there is a non-uniform trend in the time series, the MK test shows that the trend is insignificant, but the ITA method detects such non-uniform trends and makes hidden time series information available.

Rainfall is one of the factors involved in increasing soil moisture. Soil moisture, in turn, is a key parameter in the rise and fall of water in the soil which plays an important role in the rainfall-runoff process. It, therefore, requires to be carefully investigated in order to determine its effect on peak flood discharge. One method commonly used for this purpose is the CN-NRCS (curve-number method). Based on this approach, the sum of rainfalls during the 5 days preceding the flood event is taken to represent the soil moisture conditions prior to the event. Given the fact that natural phenomena are always associated with different degrees of uncertainty due to the involvement a multitude of factors, an efficient method for investigating their behavior is the Adaptive Neuro- Fuzzy Intelligent System (ANFIS). Here, we used ANFIS for determining the effect of rainfalls over the five days prior to the flood event in order to predict the maximum daily flood discharge. The model employed the two training algorithms of Back Propagation and Hybrid, which were then tested using different statistical tests and the results were analyzed for each model. The results indicate that the hybrid method outperformed the back propagation method. The best correlation coefficient of the 5-day model was 0.985 and the RMSE (Root Mean Squared Error) was 0.162 in the hybrid method.

Frequency analysis of daily rainfall or return period of rainfall and flooding events is very important considering the behavioral complexity in water resources management,because ignoring it can lead to urban destructive floods. In the present research, three distribution functions of Pearson, Beta, and Gamma were compared to investigate and select the most appropriate distribution function for the precipitation data acquired from meteorology stations and CHIRPS satellite in seven stations in the watershed of Bustan Dam. Statistical analyses showed that satellite data were ineffective to estimate daily precipitation due to high errors in RMSE, MAD, and NASH. Meteorological data were used to spot the best distribution. Google Earth Engine and Python programming language were used. Then, the selected distribution function was used to determine the maximum daily rainfall, frequency probability, and return period of 2, 10, 50, 100, and 200 years. The results of the goodness of fit test, Error Sum of Squares, Bayesian Information Criterion, Akaike Information Criteria well as Kullback-Leibler Divergence showed that in five stations of Kalaleh, Qarnaq, Golestan National Park, Golestan Dam, and Glidagh, the Pearson function is the most suitable distribution function. Also, in the other two stations (Gonbad and Tamar), the Beta function was recognized as a suitable function. However, Gamma distribution in the study area is not efficient. So, it can be concluded that heavy and irregular rainfall can be effective in choosing the best distribution function at each station. Therefore, it is recommended to consider the maximum possible rainfall and as a result of the possible occurrence of floods with principled and accurate management to prevent human and financial losses in susceptible areas, especially in the study area.

Precipitation is the most important climatic characteristic of any region. This climatic characteristic is one of the most fluctuating climatic variables that seriously affect the water resources of the region. This issue is important in Iran, where the average rainfall is over 250 mm. The purpose of this study is to analyze and explain the heavy rainfall Karkheh and Dez using statistical methods. For this purpose, precipitation data from 14 synoptic stations and a rain gauge period of 60 years (1959-2019) were used. To achieve the objectives of the research used the probabilistic distribution function the final limit type 1 Gumble, and the heavy rain threshold of each station were determined. Then to identify the uniform and non-uniform discharges in the time series maximum daily precipitation and total annual precipitation the ITA method and Man – Kendall non-parametric test were used. The results were obtained from heavy rainfall thresholds, The average rainfall of more than 40/7 mm in Karkheh and the average rainfall of more than 47 mm in Daz are considered heavy rainfall. The average rainfall in Karkheh is 118 days and the dose is 81 days. The flood threshold of Karkheh is less than the Dez catchment. Therefore Karkheh rains occur more suddenly and irregularly while Dez has a more normal time series. As a result, Karkheh is more vulnerable to floods than Dez in terms of increased heavy rainfall. The results of using the Man – Kendal, and ITA test showed that Man – the Kendal test can only detect uniform trends in time series as the advantage ITA method is that in addition to uniform trends. It can detect hidden trends and internal in identify time series. For example, although the man – Kendal test did not show a specific trend for maximum rainfall at Khorramabad station, The ITA test detected hidden and non-uniform trends for this station.

Most heavy storms result in destructive floods. One of the basic elements in analyzing floods in watersheds without data is hourly storms. The Determination of the storm of the watershed needs regional analysis of storms and transferring them to the gravity center of the watershed. Maximum daily precipitation ( 24 P ), is the most accessible storm in any region, which can be converted to hourly precipitation. The analysis of the point and regional 24 P is one of climate studies requirement. Regionalization of 24 P , can be an influential step toward analyzing storms and floods. In order to accomplish such a task, two approaches are possible, one is using the old methods of geographical regionalization and the other one is using the new methods like "Cluster Analysis" and "L-Moments Homogenous Tests". In this paper second approach was employed. All existing rain-gauge stations (N= 396) were considered and their available data were collected in this study. Basic tests were applied and 266 stations were removed due to the lack of the required conditions and only 130 stations were used in analysis. "Principal Components" method was used to omit the uninfluential variables (only 6 variables out of 21 were proved as basic and important). "Hierarchical Clustering" was used in the process of regionalization of the stations indicated of seven different regions. These regions were distributed in different locations throughout the country and the regionalization map is presented. The "L- Moments Homogenous Tests" were also employed for further indication. According to the final results, the regionalization of 24 P of Iran's rain-gauge stations can be defined as 7 homogenous regions.

Rainfall characteristics, which include spatial variability, exert a major influence on runoff properties. Many techniques have been proposed for determining the spatial distribution of daily rainfall. One of these techniques is spatial modeling, based on rainfall data measured by rain-gauge networks. In this study, application of different interpolation methods in the GIS environment, for estimating the spatial distribution of daily rainfall in the southwest of Iran with low rain-gauge density, have been compared on a regional scale. The cross validation technique was selected as an accuracy index and statistical parameters, such as MAE (Mean Absolute Error) and MBE (Mean Bias Error), were used for comparing the results of cross validation. The ranking of MAE and MBE values was used for determining the best interpolation method. The interpolation methods that were studied for mappingthe spatial distribution of daily rainfall include nearest point, moving average, moving surface, trend surface and kriging. Since the spatial pattern of daily rainfall is random, the moving average method, with inverse distance weight function, was determined as the best method for interpolating daily rainfall data in the region of study.

Erosion is defined as the separation and transference of the soil particles from the surface, which can take place by water or wind. Among the factors affecting soil erosion by water are; water or rain erosivity, soil erodibility, slope of the surface, coverage of the soil surface, and soil management. Rain erosivity index is the most well known index renderd in the universal soil loss equation (USLE) which is called as Wischmeier index (R). This index is defined as the sum of (E.I30) in which E is the kinetic energy of the rain and 130 is the maximum intensity of 30 minutes rain. in this research first a relationship between kinetic energy of the rain and its intensity was established. This work was conducted by a rainfall simulator. Then, Theran rainfall data extracted from the graphs of rain gauge record was collected. Rainfall data course was for a period of 20 years. Therefore, it was possible to calculate the total kinetic energy and then the R factor. The annual estimated average R in Tehran was 98 Mj.mm/ha/hr. Also it was possible to calculate the erosivity index for the whole year. Based upon the index of R for each rain or the annual R relationships between R and some rainfall parameters were investigated. These parameters were, amount of climate, daily rainfall, maximum daily precipitation, average 6-hour prectitation. Erosivity index for different return periods was also calculated. By this means, for which regions having the same type of the climate, the amount of erosivity index can be estimated.

One of the important relationships which are used in the estimation of river discharges and floods is Intensity-Duration-Frequency (IDF). The accuracy of this relation is dependent on the accuracy of its parameters which need to be found based on short-duration rainfall depths (such as 15, 30, 60 minutes, and so on) for a long term (i. e. 30 consecutive years). Unfortunately, only 24-hour rainfall depths are available in many rainfall stations in Iran. Various empirical relations are available to convert 24-hour rainfall depth to sub-daily. One of these methods is IMD and its accuracy in some regions is low. In this research, the IMD method was transformed into a single-parameter equation and then, this parameter is evaluated for some rainfall stations in Iran. To do this, maximum 24, 12, 6, and 3-hour rainfall depths were extracted and their frequencies were calculated using Weibull and Gumbel methods. Regional coefficients in the modified IMD method were estimated using a linear regression method. Although the power of the IMD method is 0.33, results showed that this parameter for the rainfall stations ranged from 0.28 to 0.35. To make more comparison, the IDF relation of Kordan’s watershed was calculated using the short-duration rainfall depth which was estimated using the modified IMD, and then, this IDF was compared to observed data and Ghahraman’s relation which is commonly used in Iran. The comparison showed that the modified IMD relation could estimate the short-duration rainfall data better than Ghahraman’s relation. After calibration of the modified IMD relation for various regions in Iran, the sub-daily rainfall depth can be obtained with high accuracy.