yagob dinpashoh

Evapotranspiration is one of the main elements of hydrologic cycle. Accurate determination of reference crop potential evapotranspiration (ET0) is crucial in efficient use of water in irrigation practices. ET0 can be measured directly by lysimeters or estimated indirectly by many different empirical methods. Direct measurement is cumbersome, needs for more time and costly. Therefore, many investigators used empirical methods instead of direct measurements to estimate ET0. Nowadays, the FAO-56 Penman Monteith (PMF56) method is known a bench mark for comparing the other empirical methods. For example, in the works of Zare Abyaneh et al. (2016), Biazar et al. (2019), Dinpashoh et al. (2021) and Dinpashoh et al. (2011) PMF56 method was used to estimate ET0 and comparing the outputs of other empirical methods. Many researchers analyzed trends in ET0 time series in different sites around the Earth. Among them it can be referred to the works of Sabziparvar et al. (2008), Babamiri & Dinpashoh (2015), Dinpashoh et al. (2021), Dinpashoh  (2026) and Tabari et al. (2013). ET0 can be affected by many different climatic factors such as maximum air temperature (Tmax), minimum air temperature (Tmin), relative humidity (RH), wind speed, and actual sunshine hours. Factor analysis (FA) is a multivariate method that reduces data dimensionality. In general, climatic variables have high correlation with each other. On the other hand, these variables affect ET0. The FA can be used to reduce data dimensionality in which correlated variables converted to few uncorrelated factors.

The most sustainable and cost-effective approach to enhance river water quality is by actively managing its self-purification. This study's aim is to explore potential management scenarios for enhancing the river's self-purification capacity. The QUAL2Kw model was used to simulate the water quality and self-purification capacity in Dez River in Iran. The model was calibrated and validated using recorded data of three monitoring stations along the river. Five parameters, namely DO, BOD, COD, NO3-N, and NH4-N were calculated and compared with field data. The Margin of Safety was presented and added to the value of each parameter for better water management and protection. Sensitivity analysis was conducted to identify the most influential parameters in water quality simulation for Dez River. The study presented and compared the self-purification capacity across six proposed scenarios for managing water quality. The results showed that the oxidation rate, nitrification rate, and denitrification rate were the most influential parameters in simulating water quality using QUAL2Kw. Among the scenarios considered, the fourth scenario, which included urban and industrial sewage point sources as diffuse sources, exhibited the highest level of self-purification, estimated at 2,246,170.01 kg/day. In all scenarios, the self-purification capacity for COD exceeded that of other parameters along the river, with the highest COD self-purification reaching approximately 167,034.9 kg/day.

The first step in scientific water resources management is good understanding of the temporal precipitation pattern. One of the main tools in understanding the rainfall pattern is plotting the Huff curves. This is true especially in arid and semi-arid regions encountered with water shortages. These help decision makers in understanding temporal characteristics of rainfall, which in turn can help efficient management of water resources. Temporal distribution of rainfalls interested by many investigators in the field of hydrology such as Yen and chow (1980), Loukas and Quick (1994), Todisco (2014), Huff (1967 & 1990) and many others. Furthermore, illustration of Huff curves for different rain gauge stations performed by many researchers such as Azli and Rao (2010), Awadallah and Younan (2012), Yazdi et al. (2016), Shokri-koochak et el. (2011), and many others. In a recently published work by Ewea et al. (2016) the Huff curves were plotted for the city of Makkah Al-Mukkaramah in Saudi Arabia. Based on our best knowledge, there is no comprehensive scientific work carried out on illustration of Huff curves in Great Karun River basin, located in south west of Iran. Therefore, the main objective of this study is illustration of Huff curves and analysis of storm pattern during the rainfall occurrence in the four selected stations, including the Dez dam, Abdul-Khan, Gotvand and Ahwaz. These selected stations are located in Karun River basin, Khuzestan province, Iran.

In this research relative importance of different meteorological variables that affect potential evapotranspiration were analyzed. Two stations of Zanjan and Mahneshan with at least twenty years of data up to 2021 were selected for the research. The Penman-Monteith method was used to estimate ET0. In order to study the relative importance of climatic variables the factor analysis method was used. The correlation between precipitation, means of air temperature (maximum and minimum), wind velocity, relative humidity and actual sunshine hours were analyzed. Results showed that except one item with no significant correlation (wind and precipitation) all the other correlation coefficients were significant in 5 percent level. In both stations the eigenvalues of the two first factors were greater than one, however, they were negligible (close to zero) in the cases of other factors. In Zanjan the first two factors accounted for about 80.673 percent of total variance. This value was more than 82.5 percent in the case of Mahneshan station. In both stations the actual sunshine hour was the main parameter affected ET0 followed by the Tmax, Tmin and RH positioned in second to fourth ranks. Results indicated that for the selected stations the precipitation had no effect on ET0. Plotting the position of parameters on Cartesian plain showed that the position of parameters in the two stations are similar. The findings of this study are helpful in water resources management in the region.

Accurate estimation of crop water requirement is important especially in arid and semiarid climates. The rate of evapotranspiration can be measured by a lysimeter, however, it is expensive and its measurement is a cumbersome practice and time consuming. Therefore, many researchers use empirical models instead of direct measurements. Evapotranspiration of every crop is related directly to reference crop evapotranspiration (ET0). There are many empirical models for estimation of ET0. Among them the FAO-56 Penman-Monteith (FAO56PM) is known as the standard method in every climate. However, this method needs more climatic parameters which are not available everywhere. Therefore, identification of the model which needs less parameters and easily available climatic parameters will be useful. In this study three candidate models which had such conditions considered. These three models are i) Blaney-Criddle (BC), ii) Doorenbos and Pruitt (DP), and iii) Turk. The suitability of the candidate models compared with the output of the FAO56PM method. The main objective of this study is finding the most suitable model among the three candidate methods in Urmia Lake basin.

The region under study is the Urmia Lake basin located in North West of Iran. Nine stations selected across the basin. Meteorological data gathered from the Islamic Republic of Iran Meteorological Office (IRIMO). The method used here as a bench mark for evaluation of other empirical models is FAO-56 Penman-Monteith (FAO56PM). Three empirical models for ET0 estimation which need less climatic parameters are i) Blaney-Criddle, ii) Doorenbos and Pruit, and iii) Turk. These three models need climatidata that are easily available at least in the region. The recommended form of the FAO56PM method is as follows:ET_0=(0.484×Δ(R_(n-) G)+ϒ 900/(T+273) u_2 (e_s-e_a))/(Δ+ϒ(1+0.34u_2)) (mm day-1) [1] Where Rn is the net solar radiation (MJ/m2/day), G is the ground heat flux (MJ/m2/day), T is mean daily air temperature (℃), u2 is the wind speed at two- meter height (m/s), es is the saturated vapor pressure (kPa), ea actual vapor pressure (kPa). Other parameters explained in Allen et al. (1998).The first empirical candidate model for estimation of ET0 is the Turk model (Shuttleworth 1993) which reads:ET0 =0.31 T/(T+15)(S_n+2.09)(1+(50-RH)/70 ) ( 〖mm day〗^(-1) ) ,if RH<50% [2] Where Sn is the net solar radiation in (MJ/m2/day), RH is the relative humidity (%). If the average RH of a station is great or equal to 50%, then the second parenthesis will be removed from the equation, i.e. its value will be unity. The second empirical candidate model for estimation of ET0 is the Doorenbos and Pruitt (DP) model (Shuttleworth 1993) which reads:ET0 =-0.3+b_dp Δ/(Δ+γ) S_n 〖(mm day〗^(-1)) [3] where bdp calculated from the following relationship:b_dp= 1.066-0.0013 (〖RH〗_mean)+0.045 (U_d)-0.0002 (〖RH〗_mean)(U_d)-0.000315〖(〖RH〗_mean)〗^2-0.0011(〖U_d)〗^2 [4] The third empirical candidate model for estimation of ET0 is the Blaney-Criddle (BC) model (Fooladmand and Ahmadi 2009) which reads:ET0=(a_BC+b_BC f) ) 〖mm day〗^(-1)) [5] Where f=P(0.46T+8.13) [6] and a_BC= 0.0043〖RH〗_min - (n/N)- 1.41 [7] b_BC= 0.82-0.0041 (〖RH〗_min) + 1.07(n/N) + 0.066(U_d) -0.006(〖RH〗_min) (n/N) - 0.0006 (〖RH〗_min) (〖RH〗_min) (U_d [8] In [7] and [8] n is the actual sunshine hours and N is the maximum daily sunshine hours.In order to evaluate the models performances three criteria were used in this study which are i) coefficient of determination (R2), ii) root mean square error (RMSE), and mean absolute error (MAE). The output of models compared with that of the FAO56PM output in each of the selected stations.

Results showed that the median of R2 values of the Turk and BC were great than DP. The median of R2 values of both the Turk and BC were about 0.9. However, this measure for DP was about 0.75. The variance of R2 values in the case of BC was less than DP. The lowest value of RMSE belonged to the BC model which was about 2 mm/day. This value for other two models were more than 2 mm/day. The variance of RMSE obtained for all the nine stations was minimum comparing the three models. Therefore, according to Fig. 3, it can be suggested that when the RMSE was used for selection of the best model then the TURK model was superior than the others. However, when we considered all the three criteria for model selection, then the TURK model was superior than the others. According to Fig. 6 it can be concluded that in summer hot days the DP model overestimate the ET0 comparing the FAo56PM at Tabriz station. However, in the winter cold days DP underestimated the ET0 comparing the FAo56PM at the same station.

In this study three candidate models compared with the base model i.e. FAO56PM. Nine stations around the Urmia lake selected. Results indicated that the TURK model was suitable for ET0 estimation in Urmia Lake basin. This model only need three weather parameters which are i) Tmean, ii) actual sunshine hours (n), and relative humidity (RH). Logical use of fresh water in this basin is recommended.

One of the important consequences of the climate change on extreme floods is the change in their frequency, timing and magnitude. In this research, the seasonality of flood in the Urmia Lake basin was analyzed based on the extreme flood data from 14 stations. This work was done in the statistical period of 2003-2019 using the new method of circular statistics. The uniformity of occurrence time of extreme floods (OTEF) was examined by Rayleigh-test and Kuiper-test, in three significance levels of 0.1, 0.05 and 0.01. The slope of the trend lines for the OTEF were estimated using the modified Sen’s estimator. The results of the Kuiper test indicated that there is no uniformity in the OTEF. It was found that there are two distinct flood seasons in the region including a) late March to mid-May (S1) and b) mid-September to early December (S2). The mean of seasonal strength index of events was equal to r̅=0.695. By dividing the year into above mentioned seasons, this index was obtained as 0.9 for the first season and 0.78 for the second season. The two eastern and western parts of the Urmia Lake had same seasonality strength in S1. However, in S2 the seasonality of the western part of the lake was stronger than the eastern part. In S1, on average, the OTEF in 40% of the stations had a negative trend while for the rest it showed a positive trend. For S2 the stations with negative and positive trends were respectively 11% and 78% of the total.

Detection of trends in streamflow characteristics such as low flows is so important in optimal water resources management. This is especially true in arid and semi-arid climates that water is vital for human being and all other living things. Lorestan province, located in the west part of Iran was considered as the study area. Daily mean streamflow data of hydrometric stations during the time period provided by Lorestan Regional Water Company located in Khorramabad city. Eight hydrometric stations selected for this purpose. The altitude of the chosen stations varied between 770 and 2050 m above the mean sea level. Literature review on this subject indicated that low flow trends in Lorestan province river has not been before studied. On the other hand, such a study is so important for better management of fresh water in the region, therefore, conducting this study seems to be necessary.

In the first step of this study, flow duration curves (FDC) plotted for the stations. Two indices including the Q0.05 and Q0.10 were considered here as measures of low flows. The Q0.05 index value extracted from the FDC as a five percent low flow quantile. This index shows that the streamflow discharge is less than that in five percent of the days in a year. In addition to Q0.05 the second measure namely Q0.10 is read from FDC of the selected sites. Therefore, for each site, these two indices were gathered during the used time period. Then, trends of the mentioned indices are analyzed using the Mann-Kendall method. In this regard the effect of serial correlations removed from the time series. Moreover, the slope of trend lines estimated using the Sen’s estimator approach. Then the selected quantiles fitted for suitable statistical distributions. In this regard the well-known method namely Kolmogorov—Smirnov was used.The parameters of the selected distribution estimated using the maximum likelihood method. Finally, at each site the values of low flows corresponding to different return periods i.e. 2, 5, 10, 25 and 50 years were estimated. It is worthy to mention that the missing data are not reconstructed here, because the used approach (Mann-Kendall) is a non-parametric method and no need for reconstruction of the missed values.

Results showed that two stations namely Sokaneh-Nahaee and Cham-Chit had significant first-lag serial correlation for Q010 time series. The other six sites had no significant serial correlation for this quantile. Furthermore, in the case of Q0.05, three sites showed significant first-lag serial correlations. So, the modified Mann-Kendall method was used for these time series. This analysis indicated that the mentioned series auto-correlation was significant in 5% level. The conventional MK method was used to detect trends in other time series which their serial correlations are not significant. Results showed that trends of Q0.10 quantile series in four out of the eight hydrometric stations were downward and two of them were statistically significant at 1% level. The two others had no significant trends. At the same time the other sites showed upward trends in Q0.10 series. However, among these series one station namely Cham-Chit had statistically upward trend at 1% level. Trends in the other three sites are not statistically significant.  In the case of Q0.05 series, the six out of the eight stations showed negative trends, in which two sites had statistically significant trends at 1% level. The names of these sites are Sokaneh-Nahaee and Vanaee. In contrast, the two other time series showed positive trends, in which only one of them (namely Cham-Chit station) had statistically significant trend at 1% level. The trend line slopes of Q0.10 quantile time series are ranged between -0.0844 (in Sokaneh-Nahaee) and +0.12 (in Cham-Chit). However, in the case of Q0.05, this range was between -0.0885 (in Sokaneh-Nahaee) and +0.008 (in Cham-Chit station).

Some of the stations showed upward trends in low flows in Lorestan province rivers and some others showed downward trends. It is worthy to note that the time periods of the used data of the stations are not same. Although Masih et al. (2011) reported that the mean daily stream flows (i.e. Q0.50 or 50th quantile also called median) of Zagros Mountain rivers had downward trends. Investigation of sites location indicated that no obvious pattern in trends of low flows existed in the area under studied. This is true for both two low flow indices (i.e. Q0.05 and Q0.10) used for hydrometric stations. The findings of this study would be helpful in better management of surface water in Lorestan province.

The aim of the present study is regionalization of groundwater observation wells of Khoy plain into distinct clusters based on quality of water using the K-Means method. The recorded data of fourteen groundwater quality parameters including the Total Cations, Total Anions, Electrical Conductivity (EC), pH, Total Dissolved Solids (TDS), Sodium Absorption Ratio (SAR), Total Hardness (TH), Sodium percent (%Na), Magnesium (Mg2+), Calcium (Ca2+), Sodium(Na), Sulfate (SO42-), Chloride (Cl-), Bicarbonate ) were used. These data gathered for the 26 observation wells in the time period of 2001-2003. The optimum number of clusters was found by optimization method in K-means clustering algorithm assuming to be between two and five. In order to determine the groundwater quality to use in agricultural and drinking purposes the Wilcox diagram was used. The results showed that groundwater of Khoy plain can be classified into the four distinct classes. The first class covers an area equal to 214.3 km² (51.14 % of the total area of the plains), which has very favorable to use in agriculture and drinking use. The second region covers an area of 50.1 square kilometers (11.95 %) and the third region’s area was 52.7 km² (12.57 %), respectively. The third region has poor quality water and area of this region is equal to 9.101 km² (24.31%). The high values of EC and SAR were found in the third cluster, which led to groundwater quality to be poor. In general, it can be concluded that more than the 50 percent of the Khoy plain’s groundwater had desirable chemical quality. It is recommended to protect groundwater in Khoy plain from pollution risk and overexploitation. For sustainable use of groundwater, it is recommended to protect groundwater by prohibiting agriculturalists and other users from overexploitation.

One of the standard models for estimation of ET0 that accepted by all hydrologists and climatologists is the FAO Penman-Monteith (FAO56PM) method. Although this model is accurate in ET0 estimation, however, it has some limitations. The main limitation of this method in in its need for various meteorological data, including the solar radiation, air temperature, relative humidity, dew point temperature, wind speed and actual vapor pressure. Unfortunately, all of these parameters are not readily available in all the conditions. In this regard, many researchers interested to find a simple method for accurate ET0 estimation (Sentelhas et al., 2010; Dinpashoh, 2016; and many others). Based on our best knowledge there is no comprehensive study conducted in Urmia Basin for finding a simple and accurate method that needs less weather parameters for ET0 estimation. Therefore, the main aim of this study is estimation of ET0 that needs less weather parameters in Urmia Lake basin.

The area under study is the Urmia Lake Basin, located in North-West of Iran. This basin is approximately lied between the 35⸰ 40´ E to 38⸰ 29´ E latitudes and 44⸰ 07´ to 47⸰ 53 longitudes. The area of this basin is about 51700 km2 which is equal to about 3.2 percent of Iran's area. Data used in this research are the daily recorded values of maximum air temperature, minimum air temperature, wind speed at 10 m height, relative humidity, sunshine duration, and some geographic information such as altitudes, latitudes and longitudes. The nine stations were selected from different points of the basin in this study. The FAO56PM method (Allen, 1998) was selected as the bench mark for ET0 estimation in all the stations. In this method the following equation was used for ET0 in the chosen sites.
                                                                  (1)
where ET0 is the reference crop evapotranspiration (mm/day), Rn is the net solar radiation at crop surface (MJ m-2 day-1), G is the soil heat flux (MJ m-2 day-1), T is the mean air temperature at 2 m height (°C), u2 is the wind speed at a 2 m height (m/s), the term (es-ea) is the saturation vapor deficit (kPa), Δ is the slope of the vapor pressure curve at the point of air temperature (kPa/°C) and g is the psychometric constant (kPa/°C). In order to convert U from 10 m height to u2 the following equation was used (Nandagiri and Kovoor, 2005; Sentelhas et al., 2010; Dinpashoh et al., 2011):                                                                                                                       (2)
where Uz is the wind speed (m/s) at z m height, and zw is the height (m) at which wind speed measured.
In this study, in order to find an alternative model, which uses less weather data in estimation of ET0 the three empirical models namely Hargreaves (HG), Kimberly Penman (KPM), Priestly Taylor (PT), and Multivariate Linear and non-linear regression were used. Evaluation of the models performed using the three metrics, coefficient of determination (R2), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE).

Results showed that, the median of the R2 values for KP was more than 0.986. The median of the R2 values for PT and HG models were found to be equal to 0.902 and 0.40, respectively. The median of RMSE for HG model was about 0.9 (mm day -1). This value for KPM and PT models were about 1.3 and 2.1 (mm day -1). The median of MAE for the selected stations for KPM was less than 1 (mm day -1). This value for HG was equal to 0.7 (mm day-1) and in the case of PT was more than 1.5 (mm day -1). Therefore, considering the MAE values and RMSE, the HG model was detected to be the suitable method foe ET0 estimation in Urmia Lake basin.

In recent years, rivers flows have significantly decreased due to regional or global climate change and human activities especially in the arid and semi-arid regions. In this study, the effect of climate change and human activities on the runoff responses was examined using hydrologic model simulation in the Lighvan basin located in the northwest of Iran. For determination of hydrologic model MLR methods (Forward and Ridge) were used. The Mann–Kendall test was applied to identify the trends in hydro-climatic data series. Also, the Pettitt’s test was adapted to detect change-points in the annual discharge values and climatic variables. The results showed that there was negative trend in discharge data series, so that in Hervy station it significant at 10%. Examination of the climatic factors indicated that there was an increase in the temperature values and a decrease in the relative humidity values at the basin. Also all variables related to precipitation in spring have decrease trends. The rapid changes in runoff values and most of the climatic variables occurred in mid-1990s. Comparison of the average discharge in the Hervy Station in the two periods indicates 36% decrease in the recent period compared to the natural period. The effect percentages of the human factors and climatic factors on runoff reduction in all the models used were 65%-84% and 16%-35%, respectively. Therefore, the impact of human activities on the river flow changes was significant.

In this study, rainfall and runoff data recorded of selected stations of Aras Boundary Basin were used to analyze rainfall and runoff fluctuations and they are projected for horizons, 2050. The Pettitt test was used to detect the breakpoint in rainfall and runoff time series. Trends in rainfall and runoff were also calculated using the original and modified Mann-Kendall test. To project the future, general circulation models (GCMs) under two greenhouse gas emission scenarios i.e. RCP4.5 (low emission) and RCP8.5 (high emissions) were used. The Eureqa Formulize tool was used to simulate the rainfall-runoff process. Results showed that most of the abrupt changes have occurred in the second half of the 1990s. 83% of seasonal time series breakpoints were related to runoff. Also, 67% of the abrupt changes have occurred in the winter and spring seasons. The highest increase in annual rainfall (according to RCP4.5 scenario) at Nir station is expected to be 9% and the highest decrease in annual rainfall (according to RCP8.5 scenario) at Khoy station is predicted at 11%. It is also worth mentioning that in the seasonal time scale will have the highest rainfall reduction in summer. The Eureqa Formulize performed very well at all stations with NRMSE of less than 0.5%. The results indicated that the lowest slope of the base period runoff trend line (in seasonal time scale) was -1.3 million m3 in summer at Badalan station. There will be no significant change in the annual flow in the future period.

Evaporation is one of the main elements of hydrologic cycle. Accurate estimation of pan evaporation is very important in many water-related activities such as irrigation and drainage projects, water balance studies, reservoir operation, and the like. The class A pan is one of the main pan evaporation instruments, which is used in standard synoptic weather stations in Iran. Direct measurement of evaporation is expensive and time-consuming. Therefore, different empirical models, which use different meteorological variables, can be used to estimate pan evaporation. This is so crucial in arid and semi-arid countries such as Iran, where the climate is mostly hyper-arid and it is not easy to measure evaporation directly. In the recent decades, by the development of computers many data driven models have been created for estimating evaporation. One of the intelligent models widely used to hydrologic processes is Bayesian Network Model, which was introduced by Bentin in 1990, and then applied for neural networks by MacKey (1992). Bayesian networks (BNs), also known as belief networks (or Bayes nets for short), belong to the family of probabilistic graphical models (GMs). These graphical structures are used to represent knowledge about an uncertain domain. In particular, each node in the graph represents a random variable, while the edges between the nodes represent probabilistic dependencies among the corresponding random variables. These conditional dependencies in the graph are often estimated by using known statistical and computational methods. Hence, BNs combine principles from graph theory, probability theory, computer science, and statistics. GMs with undirected edges are generally called Markov random fields or Markov networks. These networks provide a simple definition of independence between any two distinct nodes based on the concept of a Markov blanket. Markov networks are popular in fields such as statistical physics and computer vision. BNs correspond to another GM structure known as a directed acyclic graph (DAG) that is popular in statistics, machine learning, and artificial intelligence societies. They enable an effective representation and computation of the joint probability distribution (JPD) over a set of random variables (Reggiani and Weerts, 2008). In addition, BNs model the quantitative strength of the connections between variables, allowing probabilistic beliefs about them to be updated automatically as new information becomes available. In this model, the unknown relationships between parameters in processes can be shown by a diagram. This diagram is non-circular, and has directions composed of nodes and curves for showing the possible relationships in parameters (Money et al, 2012). Therefore, the main objective of this study is modeling of daily class A pan evaporation using the Bayesian Network model in six stations of East Azerbaijan Province.

Reference evapotranspiration (ET0) is a climatic parameter and can be computed from weather data. It is one of the most important hydrological parameters for calculating crop water demand, scheduling irrigation systems, preparing input data to hydrological water-balance models, regional water resources assessment, and planning and management for a region and/or a basin. The climatic data from synoptic stations with more than 20 years continues record in West Azarbaijan province was used. The well-known FAO-PM56 method was used to calculate the ET0. Then Multiple linear Regression (MLR) was used to estimate the ET0. The RMSE, MEA, NSH, and R2 were used to evaluate the performance of the MLR model. Then, the correlation coefficient (r) between ET0 and each of the meteorological parameters was obtained. And finally, with using Path analysis method, the influence of direct (P) and indirect effects of the meteorological parameters on ET0 was calculated. In the studied synoptic stations, NSH between 0.91 and 0.99,   R2 between 0.91 and 0.99, RMSE between 0.05 and 0.15, and MEA between 0.04 and 0.12 were obtained. Also, it was found that the wind speed at all of stations had a significant correlation (at the 0.01% level) with ET0. The path analysis results showed that the maximum value of P (direct effect of meteorological parameters on ET0) in all of the stations belongs to wind speed. The P value of wind speed in Urmia equal to 0.85, Piranshahr equal to 0.99, Takab equal to 0.97, Khoy equal to 0.90, Sardasht equal to 1.06, and Mahabad equal to 0.78 are obtained.

A better understanding of trends in reference crop evapotranspiration (ET0) is crucial, in scientific management of water resources, in arid and semiarid regions. According to the fifth assessment report of the Intergovernmental Panel on Climate Change (IPCC), the global warming trend, which is mainly caused by the increasing amount of greenhouse gas emissions, will be continued. Climate change is known as a global environmental challenge facing humanity with implications for food production, natural ecosystem, and fresh water supply. The expected climate change is thought to have a severe impact on different elements of natural systems such as agriculture, hydrology, and ecosystem. reference crop evapotranspiration is one of the main elements of hydrological cycle affected by climate change. reference crop evapotranspiration can be considered as a measure of atmospheric evaporative demand. It is independent of crop type, crop development, and management practices. It provides a measure of the integrated effect of several meteorological parameters such as radiation, wind speed, air temperature, and humidity. reference crop evapotranspiration variability in a single station is affected by these climatic parameters. Estimating reference crop evapotranspiration is one of the important steps for calculating crop water requirements that has a special economic importance in the rationalization of water consumption in the agricultural field under current and future climate conditions. Moreover, this parameter plays an important role in the energy balance of basin ecosystems. Several hydrological processes, such as soil moisture dynamics, groundwater recharge, and runoff generation affected by ET0 fluctuation. 

The data of the 18 synoptic stations located in the west and Northwest of Iran were obtained from the Islamic Republic of Iran Meteorological Organization (IRIMO). In this study, the stations which had at least 20 years of daily data (up to 2016) were chosen for analysis. The gathered data including the meteorological parameters namely maximum air temperature (Tmax), minimum air temperature (Tmin), mean air temperature (Tmean), wind speed in 10 m height (U), maximum relative humidity (RHmax), minimum relative humidity (RHmin), sunshine hours duration (n), and actual vapor pressure (ea). Each of the mentioned data was checked for quality, separately. These data were used to estimate the daily values of ET0 in selected stations using the FAO-56 PM method. The trends of ET0 were detected by using the Mann–Kendall test. The slopes of the trend lines were computed by using the Sen’s slope estimator. And, to investigate the spatial and temporal variability the IDW interpolation method was used

The results showed significant increasing as well as decreasing trends in the annual and monthly ET0. Although, the increasing trends in ET0 was more pronounced than the decreasing trends. In the monthly scale, during the warmer months of the year, the observed increasing trends were more than the decreasing trends of the ET0. In the annual scale, the stronger positive trend in ET0 magnitude was found at Kermanshah stations (Z=5.79), and the strongest negative trend was found at Khodabandeh station (Z=-1.78). Also, in the monthly scale and in the warm season, the strongest positive trend magnitude was found in August at Kermanshah station, (Z= 5.43), and the monthly strongest negative trend magnitude was found in August at Khodabandeh station, (Z=-3.47). In general, it is possible to conclude that, in the recent decades the required water of the plants is increased in the studied area.

Reference crop evapotranspiration is one of the main elements of hydrologic systems. Climate change in different parts of the Earth impacted natural systems in a different way. This study examined the trends of ET0 in 18 weather stations selected in west and northwest of Iran. The FAO-56 PM method used to calculate the ET0. The MK method was used to detect the trends in monthly and annual ET0 time series.The Sen’s estimator was used to estimate the magnitude of the trends. Results indicated that most of the monthly ET0 time series had upward trends. In annual time scale, Most of the stations showed increasing annual ET0 trends, which were significant at 10 percent level. Therefore, it can be concluded that in all water-related activities, especially in agriculture, fresh water should be used scientifically. Otherwise, all of the water-dependent activities might be adversely affected in future.

In this research, projection of precipitation in the three distinct 20-years future periods (i.e. 2021-2040, 2041-2060, and 2061-2080) was performed using the LARS-WG6 statistical downscaling model. For this purpose, two scenarios of the IPCC fifth assessment report (namely RCP4.5 and RCP8.5) and MPI-ESM-MR general circulation model, which is known to be a CMIP5 coupled models were utilized. The precipitation trends were analyzed in the base and future periods using the Mann-Kendall method for both seasonal and annual time scales. Sen’s estimator method was used to estimate the slopes of trend lines. The results showed that winter precipitation will be increased during the three considered future periods. Moreover, in the spring and autumn, according to the RCP8.5 scenario, precipitation will be decreased in all future periods. The precipitation in December and January would be increased in all three future periods using both scenarios. March, July, September, and October will also experience a decline in precipitation in the three future periods, according to both scenarios. The mean annual precipitation in the future period of 2061-2080 would be decreased based on both scenarios. The highest reduction in precipitation would occur in the period 2061-2080 belonged to the RCP8.5 scenario in which the amount of reduction in mean annual precipitation is equal to 10.4%. In addition, based on the RCP4.5 scenario, the highest increase in the average annual precipitation during the future period of 2041-2060 was equal to 8.1%. There was no significant trend in precipitation series at 5% level. The slope of the trend lines in the base period and the future periods, based on the scenario RCP8.5, was found to be negative in all seasons. While in the future period, based on the RCP4.5 scenario, the trend line slope was positive for in all seasons.

This study aims at plotting the Huff curves and designing storm hyetographs in the stations of Izeh, Idonak, Abdolkhan and Ahvaz. A total of 1811 recorded storms in the period 1966-2016 in different seasons were classified into five distinct time groups according to their rainfall duration. The Huff curves were plotted for each class in each of the seasons using the whole set of storms. Results showed that classification of storms led to a better distinction of rainfall pattern in different seasons and durations. In order to compare the time distribution of rainfalls, three indices of S, I, and Q were defined that consider the ratios of non-dimensional cumulative rainfall curves from the 10% probability Huff curve obtained in the 25%, 50%, and 75% of time durations to their corresponding values from the 50% probability Huff curve. The results showed that in the four mentioned stations, the values of S index were greater than I, and both of them were greater than Q. The range of S index varied from 1.47 (in Idonak station for spring storms having the duration between 12-24 hours) to 9.63 (in Abdolkhan station for spring storms with the duration of less than 2 hours). Whereas the range of Q index varied from 1.03 (in Ahvaz station for spring and winter rainfalls having the duration of less than two hours, and in Idonak station for spring storms with the duration of less than two hours) to 1.44 (in Abdolkhan station for spring storms with the duration of 6-12 hours). The range of I index varied from 1.07 (in Ahvaz for spring storms with the duration of 2-6 hours) to 2.12 (in Abdolkhan for winter storms with the duration of less than two hours). For each of the Huff curves, design storm hyetographs were derived and presented using the 50% probability Huff curve.

Ghezel Ozan River Basin is one of the important basin in Iran, which supply people grains requirements. The amount of potential reference crop evapotranspiration (ET0) was evaluated with RCP4.5 (low emission) and RCP8.5 (high emission) scenarios on the horizons 2030, 2050, and 2070. The output of four GCM models in CMIP5 and the LARS-WG6 statistical downscaling were used. In this study, the daily historical records of six synoptic stations (namely Zanjan, Mianeh, Khalkhal, Zarrineh, Qorveh, and Bijar) from 1989-2016 were used. Differences of mean ET0 time series in the base and future time periods were tested using the t-test method in three-time scales (i.e. monthly, seasonal, and annual scales) at 5% significance level. Trends of ET0 in the proposed three-time scales were analyzed in the base and 2021-2080 periods with both RCP scenarios using the Mann-Kendall (MK) method at 5% significance level. The effect of significant autocorrelation coefficients was eliminated in MK method. The slope of trend lines was estimated by Sen’s estimator. Results showed in the whole basin, based on the RCP4.5 scenario in the horizons of 2030, 2050, and 2070, the amount of ET0 will be increased by 1.8%, 3.7%, and 5.7%, respectively. These records were about 1.7, 5.4, and 9.1 percent using the RCP8.5 scenario, respectively. The most increase in ET0 was observed for July. The annual ET0 values would be increased in the future in all stations. The mean differences of ET0 in June, July, August, summer, and annual time series with respect to the base time period were significant for all the stations and for all the future periods (under two RCP scenarios). In the future period, according to the both scenarios at all stations, the annual ET0 trend was upward.

Accurate planning for adaptation to climate change is very important in each region. In this study, using the meteorological data of the six synoptic stations in the Ghezel Ozan basin in the period 1989-2016, and by employing the four GCM models, under the two scenarios RCP4.5 and RCP8.5, data were generated for the horizons 2050. Then, some parameters such as the air temperature, precipitation, potential evapotranspiration (ET0), precipitation deficit (PD) during the growing season, dryness intensity were calculated. ET0 was calculated by Pristeley-Taylor (PT) and Penman-Monteith (PM) methods. Then, ET0 obtained from the PT method was calibrated using four Artificial Intelligence methods (namely Eureqa Formulize, ANN, ANFIS and SVM) with PM method for each station. For spatial analysis, three geostatistical methods namely IDW, Kriging, and Cokriging were utilized. The results indicated an increase of 0.9 - 2 ºC in mean air temperature and an increase in precipitation between 27 and 49 mm will be experienced in the future period. Furthermore, ET0 and dryness intensity will be increased at all the stations. The increase in average PD (in the whole basin) will be about 6% to 9%. In average, the rate of increase in agroclimatic indices in the RCP8.5 scenario will be about four percent more than the RCP4.5 scenario. Among the methods of interpolation, the modified Cokriging based on DEM (Digital Elevation Model) showed the more suitable one among others. The length of the growing season will be elongated from 15 to 35 days. No significant changes will be occurred for dryness period. The spatial variation of future climate variables is expected to be not changed comparing the base period.

Introduction Reference potential evapotranspiration (ET0) is one of the main elements of hydrologic cycle which can be estimated from weather data. This element can be used in calculating crop water requirements, scheduling irrigation systems, preparing input data to hydrological water-balance models, regional water resources assessment, and planning and management of water in a region and/or basin. The use of ET0 permits a physically realistic characterization of the effect of the microclimate of a field on the evaporative transfer of water from the soil-plant system to the atmosphere. It provides a measure of the integrated effect of radiation, wind speed, temperature and humidity on evapotranspiration. The long-term mean ET0 value in a certain time scale (month, season or year) can be changed during the recent decades in a given station. By decreasing ET0, crop water demand decreases, too. Conversely, by increasing ET0 the crop water requirements increases accordingly. Therefore, it can be suggest that change in the rates of ET0 due to climate change would have great importance to agriculturalists and water decision makers. On the other hand, accurate estimation of ET0 is crucial in improving the irrigation efficiency in a region. Many climatic parameters impacted the ET0 value in a single site. On the other hand these parameters are correlated to each other. Materials & Methods The climatic data from the synoptic stations with at least 20 years of continues records in East Azarbaijan province gathered from the Islamic Republic of Iran Meteorological Organization (IRIMO). The obtained data include maximum air temperature (Tmax), minimum air temperature (Tmin), wind speed in 10 m height (U), maximum relative humidity (RHmax), minimum relative humidity (RHmin), and duration of sunshine hours (n). The well-known FAO-PM56 method was used to calculate the ET0. There are many methods for ET0 estimation. The Penman–Monteith (PM) method is recommended as the standard by the United Nations Food and Agriculture Organization (UNFAO) and has gained worldwide acceptance and received much research interests. The PM equation has been widely used in ET0 estimation. However, this method needs more meteorological data which is not available in many regions. This led scientists to use other methods which do not need more parameters. Among the empirical methods which estimate ET0 using less climatic parameters are Hargreaves, Tornth-Wait, Belaney-Criddle and Priestley–Taylor. Unfortunately, output of these models are not accurate in all the sites. Therefore for using these simple empirical models the calibration process should be done as well. Therefore, the following issues need urgent study: (1) selection of as few dominant meteorological variables as possible meteorological parameters affecting ET0, and (2) universal application of an established model in more regions. The alternative method namely multiple linear regression (MLR) can be used to estimate the ET0. In order to evaluate the performance of the MLR method some measures calculated by comparing the results of MLR with FAO56-PM method. These measures are the root mean square error (RMSE), mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE), and the coefficient of determination (R2). Then, the correlation coefficients (ryxi) calculated between the ET0 time series (y) and each of the meteorological parameters (xi). Then, the partial correlation coefficients (rij) calculated between the explanatory variables (xi and xj) as well. Both of the direct and indirect effects of each climatic parameter on ET0 evaluated by path analysis. These effects are denoted by P and Rdc, respectively. By solving the Eq. 6 the elements of P (direct effect of xi on y or ET0 ) are obtained. By multiplying the obtained P vector (direct effects) on r_(x_i x_j ) the indirect effect of xi through the xj on ET0) were calculated. This process repeated for all the selected sites. Path analysis was first proposed in 1921 as a mathematical and statistical method by the geneticist Sewell Wright. Nowadays, the method is broadly used in agriculture and energy demands, revealing direct or indirect relationships between some morphological characters. However, little information is available on the use of this technique to evaluate the affecting factors of ET0. Given the fact that all the meteorological variables are strongly correlated and ultimately lead to multi-collinearity, traditional trend and correlation analyses cannot quantify the interactions among the meteorological factors when filtering the suitable parameters. Path analysis is a type of multivariate statistical analysis for studying relationships among variables, and it can reveal the strength of effect of independent variables on a dependent variable. Path analysis can determine direct and indirect effects of independent variables on the dependent variable, multi-collinear independent variables resulting from their own strong correlations, and optimal regression equations without unnecessary independent variables. The path coefficient is a type of standard partial regression coefficient (without units) that expresses causalities among related variables, and is also a directional correlation coefficient between independent and dependent variables. This analysis conducted for each of the selected stations in East Azarbaijan province, Iran. To do this firstly correlation coefficients between each of the climatic parameters and ET0 time series calculated. Similarly, correlation coefficients matrix between the climatic parameters which affect ET0 obtained for each of the stations. Results and discussion Results showed that the values of MAPE obtained for the stations were between 0.433 and 0.874. However, the R2 values were between 0.972 and 0.9953. Similarly, the RMSE were between 0.042 (mm/day) and 0.982 (mm/day), and the obtained MAE values were between 0.033 and 0.057, respectively. Also, it was found that the wind speed at the stations namely Tabriz, Jolfa, Sarab, Sahand, Maragheh and Mianeh had significant correlation (at the 0.01% level) with ET0. The strongest correlation detected in the station Ahar, which was between ET0 and the wind speed (at the 0.01% level). The results of path analysis showed that the maximum value of P (direct effect of meteorological parameters on ET0 belonged to the wind speed. The P values of wind speed in the stations Tabriz, Julfa, Sahand, Sarab, Maragheh, and Mianeh were equal to 0.637, 0.787, 0.877, 0.578, 0.850, and 0.780, respectively. In the station Ahar, the highest value of the P observed, which belonged to the Tmax (equal to 0.398).

Accurate estimation of ET0 is very important from the view of optimal water management in any region. Wind speed was found to be the dominant direct climatic parameter due to having the largest value of the P. In general, it can be concluded that the causal analysis method can be considered as an effective way to investigate the direct and indirect effects of meteorological parameters on ET0. Overall, it is more reasonable and scientific to apply path analysis method to evaluating dominant meteorological parameters which affect the ET0 in direct and indirect manners. The further research can be oriented in analysis on why dominant factors vary with meteorological stations. Development of other soft computing techniques which calculate ET0 using the climatic methods (such as firefly algorithm, artificial neural networks, support vector regression, and genetic expression programming) and comparing their accuracy with that of the MLR recommended for further studies.

Providing design hyetograph is an important issue in accurate determination of urban drainage networks. One of the important relevant problems of floods, is its safe transmition without any damage to facilities, farms, habitat buildings and so on. This needs accurate determination of flood quantity and then dimensions of water pass ways, bridges, flash walls, culverts, and so on. The aim of this research is plotting the Huff curves and design storm hyetographs in the six selected stations in upstream of Karkheh dam watershed. In order to design of Huff curves, the recorded date of Kamiaran, Abdanan, Darreh-shahr, Kerned, and Kermanshah were used. For this purpose, the 1191 recorded storms classified in different seasons and in five classes of rainfall durations. The Huff curves were illustrated using the mentioned information for each of the classes as well as the seasons. Furthermore, all the events in a given class and season merged in a universal distinct class and then their Huff curves were plotted too. In order to possibility of comparison of temporal distribution of rainfalls in stations, three new indices denoted by S, I, and Q were defined, each of them shows the ratio of cumulative rain depths received in 25, 50 and 75 percentages of storm durations extracted from the 10 percent Huff curves to the corresponding values obtained from the 50 percent Huff curve.  Results showed that nearly in all the stations the quantity of S-index was greater than I-index, and both of them were greater than Q-index. Results of this study have practical application in surface water management in the watershed area.

In this study, the Huff curves were extracted using the 418 events in the four selected stations. Firstly, the total storms were classified into the four distinct classes according to their durations including i) 0-2, ii) 2-6, iii) 6-12 and more than 12 hours. Then, the Huff curves were plotted for the 10%, 20%, … and 90% non-exceedance probabilities. Analysis conducted for each of the classes, separately, for the stations. Another Huff curve plotted using the all events in a unit class. Some statistical distributions commonly used in hydrology were utilized. The three indices (S2/10, I2/10, and Q2/10) calculated. The design hyetographs for each of the selected stations using the information of all events in a unit class prepared for 2 and 10-years return periods. The mathematical models of Huff curves derived as the Logistic model. The parameters estimated for all models. Results indicated that except Sarab, having the first quartile precipitation type, the three other stations had the second quartile types. The same results obtained for the class of storms with duration less than two hours. But for the classes of 2-6 and 6-12 hours, in some stations the type of precipitation shifted to the further quartile. The vertical distance of 50% and 90% Huff curves in the first, second and third quartiles shortened as the quartiles increases (S>I>Q). It was found that the Logistic model is capable in fitting the curves. The correlation coefficients between the observed and modeled values were found to be from 0.978 to 0.998.

Water is an important element of all living things. Availability of fresh water in any region is very important. Therefore, understanding the rainfall characteristics is so crucial in water resources management. One of the main tools in analyzing storms is Huff curve. Many investigators used this method for rainfall analysis with different duration. The main aim of this study is plotting and analyzing storms characteristics in the five stations namely Ajabshir, Azarshahr, Bonab, Bostan-Abad and Ligvan. In this study, using the 517 storms in the selected stations (located in the East of Urmia Lake), the Huff curves were extracted. The time period used is from 2001 to 2015. Quality of data was checked carefully prior to analysis. In the first step, the total selected storms were classified into the four distinct classes according to their rainfall duration including i) 0-2, ii) 2-6, iii) 6-12 and more than 12 hours. Then the Huff curves of each category were plotted for different probabilities of 10 percent, 20 percent, … and 90 percent. Analysis conducted for each of the classes, separately. Moreover, the Huff curves were plotted using the information of all events (i.e. without classification). In this study, some commonly used statistical distributions in hydrology were utilized. The three newly defined indices namely S, I, and Qwere defined and used in the present study. The design storm hyetographs for the selected stations and all the events (without classification) prepared for 50 percent Huff curves. The mathematical model of Huff curves were extracted as the Logistic model. The model parameters were estimated using the Curve Expert software. According to the 50 percent probability for Huff curves, the following results were obtained. For the short- time (0-2 hours) storms, the most proportion of rain received in the first and second quartiles. In the first quartile, between 28 to 44 percent of the total rainfall depth received in the selected stations. In the other words, short storms initiated with high intensity and followed by mild intensity. In the case of 2-6 hours storms class, in the two stations, a large portion of the rain (about 34 up to 39 percent) received in the first quartile. However, in the other two stations about 31 up to 34 percent of total rain received in the second quartile. In the station namely Ligvan (about 28percent of total precipitation depth) received in the third quartile. In some of the stations, and in the case of rainfall duration class of 2-6 hours storms starts with high intensity. However, in some of the other sites rain begin with mild intensity. In addition, for the storms with 6-12 hours duration, three stations can be included in the second quartile, because about 31percent of total precipitation received in this time quartile. However, in the two stations, (about 29 up to 33percent of the precipitation depth) received in the third quartile. In the class of duration 6 to 12 hours, storms begins with mild intensity and the intensity of rain increases as time advances then, finally the intensity of rain decreases till rain ceases. In addition, it can be concluded that for the storms with duration of more than 12 hours, for the station namely Azarshahr a large portion of precipitation (about 35percent of precipitation depth) received in the first quartile. Furthermore, in the two stations about 30 percent of total precipitation received in the second quartile. However, in a station namely Ligvan about 32 percent of total precipitation depth received in the third quartile. In other words, storms with duration of more than 12 hours, different stations had different temporal patterns. Based on 90 percent probability Huff curve, it was found that in the case of short- time storm class, almost in all of the stations, rainfall begins with mild intensity. Then the intensity increases gradually to reach peak in the end of the third quartile. In the 25 percent of remaining time (i.e. the last quartile) the intensity decreased again until the rain terminated. For the rainfall classes of duration more than 2 hours, precipitation reaches to the peak in the last quartile. In the other words, the precipitation begins with low intensity and gradually increases its intensity till the end of rain. In this study, three new indices that represent the ratio of precipitation at 50 to 90 percent probabilities were introduced and the values of these indices were calculated for the selected stations. It can be concluded that the most portion of rainfall received in first quartile and or second quartile for storms having duration less than 6 hours. Whereas for storms with duration more than 6 hours, rainfall started with low intensity and then the intensity increased through the rainfall duration. The results indicated that at all of the stations and for each of the duration time classes, the order of changing the values of S, I and Q indices was as S>I>Q. The modeling of the cumulative percent of precipitation as a function of cumulative percent of rainfall duration time performed using the Logistic model for each of the time classes and then its parameters were calculated which are presented in the Table 4. Based on the results, it was found that the Logistic model is able to fit the mentioned curve very well for all of the selected stations. The correlation coefficients estimated between the observed and modeled values were found to be between 0.978 and 0.998 for the sites. The results of this study anticipated to be useful in design of urban drainage structures and rainfall- runoff modeling.

Sensitivity analysis of reference crop evapotranspiration (ET0) is crucial for improving water management in the arid and semi-arid country as like Iran. However, it is important to analyze the sensitivity of ET0 to meteorological parameters, since the climate globally has been changed to some extent. In this study, sensitivity of ET0 by varying the climatic parameters at 36 selected stations in the West and Northwest of Iran was investigated. The priority and effect of the climatic parameters in different months at the selected stations were found by sensitivity analysis. The ET0 is calculated based on the most recommended form of the FAO-56 Penman-Monteith method. To analysis the sensitivity, variations of ET0 depends on the changes in minimum temperature (Tmin), maximum temperature (Tmax), wind speed (u2), minimum relative humidity (RHmin) and maximum relative humidity (RHmax), in the range of ±20% with the step of 5% was calculated. Finally, the parameter with higher importance for each station was obtained. Results showed that ET0 was more sensitive to the variation of Tmax at the 13 stations (36.11%) in annual time scale. The maximum change of ET0 by increasing of Tmax with+20% was found at Ardebil (15.54%) and the minimum change in the same situation was found to be 6.05 % at Meshkinshahr. The range of the changes by varying T min was between -47 % (in Sanandaj) to 0.91 % (in Khalkhal).

Drought refers to a period of time when water shortage occurs and, therefore, the environment and human life are disrupted. Of course, depending on the regional considerations and the objectives of any research, drought can have different definitions since the lack of water in different regions is defined differently. Drought forecasting is almost impossible and is usually a phenomenon that progresses slowly. As a result, well-timed detection in the early stages makes it possible to reduce the adverse effects on different parts of the environment, agriculture, water resources, etc. Drought characteristics such as duration and severity can be determined by drought indices. Scientists have proposed various indexes to assess this phenomenon. Drought index is a useful tool to assess drought characteristics. Effective Drought Index (EDI) is a new methodwhich is based on the cumulative daily precipitation and uses a weighting method.

Study of various aspects of daily rainfalls is so crucial from the view of scientific management of water resources in every region. Iran is located in subtropical high-pressure belt, which had low annual rainfall. The precipitation regime is very irregular both in time and space. The East and West Azarbaijan provinces are known as the important areas of agriculture, especially cereal production in Iran. Therefore, study of temporal and spatial distribution of daily rainfalls is very important in this region. The purpose of this study is to extract the best model for normalized rainfall curves (NRC) in the four selected stations namely, Tabriz, Maragheh, Urmia and Mahabad.
In this study, daily rainfalls of four stations namely, Tabriz, Maragheh, Urmia and Mahabad were used to fit the normalized rainfall curves (NRC). For this purpose, the two custom hydrologic models i.e. and were employed for NRCs. In order to find the values of (cumulative percentage of daily rainfalls) firstly the amount of daily rainfalls observations were arranged in ascending Order. Then, cumulative percent of rainfall calculated during the time period. The NRC curves of each station, plotted by drawing the versus for a total statistical period, separately. This was done for a given month (eg, January) data across the whole period and whole day's rainfall during the consecutive months of the years of the study period. In the latter case, the daily rainfalls of the first month of the first year of the study period were written consecutively in a distinct column of Excel spreadsheets. Then, daily rainfalls of the second year were written similarly, following the first years data. Daily rainfalls of the third, fourth and so on were written consecutively in the same mentioned column of Excel spreadsheets. Similarly, another column attributed to the number of rainy days in the studied period. Then, the values of non-zero daily rainfalls (arranged in ascending order) accumulated consecutively, and the resulted value were divided to the total number of observed rainfalls in the period (R). Similarly cumulative rainy days were divided to the total days (N). Moreover, the other fifteen models (including the power, exponential ...), were tested for the stations observations separately. Among the mentioned models, the most suitable one is selected according to RMSE and criteria.
Results showed that the maximum amount of daily rainfall experienced in Mahabad station in the rainiest month of the year or April (equivalent to 68 mm per day). The minimum value of daily rainfall belonged to the August (equivalent to 6 mm per day). The shape of NRCs created in this study for period in each of the four stations, showed that these curves were concave in almost all of the cases. This implies that a small amount of rainfall fell in a long period. In addition, the results showed that nearly in all of the stations the model of had the lowest value of RMSE and the largest value of . Therefore, this model selected as the most suitable one for NRCs of the stations. Although, the Exponential Association (3) model (in Tabriz) in April and the 4th degree Polynomial model (in Mahabad) in August selected as the most suitable model for them. Furthermore, the difference of statistics for the two models (at both of the time series) obtained as less than 0.0001. In the rainiest month and driest month of a year, the range of RMSE varied between 0.2559 mm in April (Maragheh) and 0.6709 mm in April (Tabriz). Moreover, the values varied between 0.9992 in August (Maragheh) and 0.9999 in April (Maragheh). In general, it can be concluded that the amount of precipitation receives in half of the rainy days is less than fifteen percent of the total rainfall depth. In this study, the values of of the most appropriate model for Tabriz, Urmia, Maragheh, Mahabad obtained as equal to 0.9996, 0.9997, 0.9996 and 0.9994, respectively.
Among the 17 candidate models, the model number 2 showed the highest , and the lowest RMSE. Therefore, the model was selected as the most appropriate model for drawing NRCs. Also, the mentioned model, were selected as the most appropriate model for all the months (in the four stations). The results showed that the NRCs were concave and in most cases, a small amount of total rainfall fell during the large number of days. In addition, in the two stations namely, Tabriz and Urmia the amount of rainfall receives in the 25, 50, 75 and 90 percent of rainy days were about two, 10, 30 and 60 percent of the total rainfall depth, respectively