جستجوی مقالات مرتبط با کلیدواژه "probability distribution function" در نشریات گروه "کشاورزی"

Standard precipitation index (SPI) is the most widely drought monitoring index. However, this index only uses the gamma distribution function for fitting precipitation data and does not consider seasonal variations. The purpose of this study was to evaluate the efficiency of SPI in drought monitoring of arid and semi-arid regions of Iran and fix the related problems with this Index. Then the SPI was compared with its modified state (SPImod) over (1956–2010). The results showed that the generalized extreme value distribution function in more than 57% of the cases was the most appropriate probability distribution function of rainfall data. But the default distribution (Gamma) was selected only in 11% of months. Comparison of Kappa index showed that with increasing time window, the agreement between SPImod and SPI indexes increases. The amounts of one-month Kappa for studied stations was Tehran (0.31), Mashhad (0.33), Bushehr (0.32) and Khorram-Abad (0.26), while for nine-month the Kappa increased. Such that in Tehran (0.49) and in Mashhad, Bushehr and Khorramabad, respectively, with values (0.47), (0.56) and (0.45). Also, the results showed that the frequency and displacement of drought classes would be very variable in comparison to these two indices. As the displacement of normal, severe drought and severe, with a total of 259, 147 and 111 events in the time window-three and displacement of moderate drought, normal and moderate wet year, with a total of 68, 54 And 28 events in time window-nine were noticeable.

Drought study and forecasting requires accurate monitoring of this climate risk. Standard precipitation index (SPI) is the most common index in drought monitoring. But there are some shortcomings, such as the lack of seasonal changes, the problem of self-affiliation in the high time series, and the consideration of the gammachr('39')s distribution function for all-time series. In this research, to resolve the bugs of SPI, it was tried to first select the appropriate distribution of precipitation from 8 different distributions. Secondly, the modified standard precipitation index (SPImod) was used to resolve the seasonal variation problem. The SPImod and SPI indexes were compared in five stations from different parts of Iran with different temperature and humidity conditions during the 55-year period (1956-2010). The results of the most suitable probability distribution function of precipitation data showed that the gamma function was not one of the selected functions in any of the cases and that the General-pareto, Weibull, and Generalized extreme value functions were the most suitable fitted distribution functions at the stations under study. Comparison of SPI and SPImod correlation coefficient showed that increasing the time series, increases the correlation coefficients. In the wet areas, the two indexes are more similar to each other. Based on the findings, there was a significant difference between SPI and SPImod at all stations, which was less significant at time series than one, three, and six months at a much higher level than in the time series Over the last 12 months, the two indexes almost matched each other. The results also showed that the difference between these two indexes was more pronounced in dryer stations. SPI seems to monitor dryness, especially in dry areas rather than droughts, so the use of SPImod instead of SPI provides more precise results due to the elimination of seasonal effects of precipitation.

This research uses the generalized gamma family models to estimate the precipitation in the high and low rainfall regions of Iran during the wet seasons in the southern and northern coast during 1986-2016. Hence it provides an applied model for interpretation and forecasting of wet conditions in future. Through this study, we have used the generalized gamma (3 parameters gamma), gamma, Weibull and the log normal models. To select the best fitted model we used some criteria such as the AIC and the BICand the k-s test has been applied for the goodness of fit test in R software. Finally the best fitted models have been used for computing the maximum event in return periods from 2 to 100 years of the southern and northern coast. The results also showed that the Weibull distribution had the best performance of the stations of the Oman sea coastal while the gamma model had the better fitting at the stations in the middle part of the Persian gulf coast. In addition, the generalized gamma model had the best fitting in the high rainfall stations in the north of the country and the stations in the west part of Persian Gulf coastal. The outputs and techniques which used through this research can be used basically for selecting the suitable distribution functions for fitting on the precipitation data during the wet seasons in the southern and northern coast of Iran.

Drought monitoring by the Standardized Runoff Index (SRI) presents some uncertainties, mainly dependent on the choice of the probability distribution used to describe the cumulative precipitation and on the characteristics of the dataset. In this study, uncertainty analysis for estimation of the hydrologic drought characteristics (intensity, duration and frequency) was performed. Four distribution functions, two time period (30 and 49 years), six time scales (3, 6, 9, 12, 24 and 48 months) and Latin hyper cube sampling (LHS) method ware used. For each event at per year and month, was generated 50000 random sampling.Then, lower and upper bands of certainty was calculated for confidence level of 95% . In addition to the drought characteristics (intensity, duration and frequency) were calculated for six time scales, four distribution functions and two length of time series . Investigation of the longest duration and highest intensities showed that an increase time scale led to decrease the frequencies of drought classes and as a result increase drought intensity and duration . Further, no significant difference in the assessment of intensity and duration was between various distribution functions, meanwhile significant difference was between normal compared to weibull and gamma for the estimation of drought frequency in short time scales (3 and 6 months). Results of this study emphasized that considering drought intensity and duration, the normal distribution function, 24-month time scale and 30-years’ time series had the largest uncertainty for hydrologic drought estimation.

The study of drought as a natural phenomenon that affects the lives of most people is very important. According to researchers in the field of drought, rainfall, temperature, evaporation, wind and relative humidity have been shown to play an important role in drought. The low variety of data required and the simplicity of calculating the SPI index led to its widespread use. The effect of increasing temperature in drought intensification is far more than the decrease in rainfall, which can confirm the effective role of temperature in strengthening or weakening of drought. Based on this, the SPEI index can be used as the appropriate index for determining the drought. In our hydrological studies, we try to fit the empirically measured data into a proper fitting function. And the best function that matches the data is chosen as the probability distribution function to derive the value of the variable for each probability. This research seeks to find the best distribution function for the SPEI index at the stations studied in Tehran province and also compares the SPI and SPEI indices at different time intervals. In this research, monthly precipitation and temperature data were used for Shemiran, Abali, Mehrabad and Tehran stations in Tehran province in 2017-1987. After qualitative control and correction and completion of statistics, statistical analysis of precipitation, based on the standardized precipitation index (SPI) and statistical analysis and dispersion analysis, are based on the standardized precipitation evapotranspiration index (SPEI). The values of the SPEI index are calculated using four Fatigue life, Weibull (three parameters), Loglogestic and kumaraswamy functions. Relationships (1) and (2) and (3) and (4) are used to calculate various cumulative distribution functions in the SPEI of the index. Fatigue life Weibull Log logistic kumaraswamy In order to investigate the most suitable distribution function compatible with Di, P-value comparison was performed based on Kolmogorov –Smirnov test ،Also to check the compatibility of the two indexes, graphs were plotted 24,12,6,3,1 and 48 months. To find out the degree of compatibility, we used the absolute value graphs of Difference of Two Indices. The results of computing and comparing the SPI and SPEI index indicate that in general, all stations in a drought condition are largely consistent and only in short periods of this adaptation are confused. Also, in comparison to the severity of drought between the two indices, the SPI index shows a lower intensity of drought and it can generally be concluded that the SPEI index shows the dry weather in terms of severity. Also, this index shows the beginning of drought in shorter time intervals, which can be attributed to the sensitivity of the SPEI index to rainfall variations and to include the temperature parameter in this index. In the short intervals, two indicators have a better match, and in the long term (24-48 months), the two indicators do not fit well. Abali station displays the best fit with the least error in all time intervals. The reason for the suitability of the Abali standardized evapotranspiration index station to show the overlap between the two SPI and SPEI indicators is the maximum rainfall and the minimum temperature and minimum evapotranspiration between stations however, it can be concluded that the drought index is well-matched in wet weather conditions with low temperatures. The difference between the two indicators in the hardest case in 1997 was 0.63, which means that each year, when the standardized rainfall index is reduced, the Standardized Precipitation Evapotranspiration Index is also declining. It can be concluded that these two indicators are in good agreement at this time interval and one can estimate one with a mean error of ± 0.209on the other consequently, reducing or increasing rainfall can directly affect the reduction and increase of evapotranspiration and temperature. In this research, it is assumed that, in addition to the spatial variation that causes changes in the statistical distribution, the annual variations of Di also confirm this hypothesis So, in calculating droughts or other climate studies, this should be considered, since rainfall, evapotranspiration, and temperature vary in different seasons, and therefore, in terms of statistical distribution, they act differently, for example The stations under study in Tehran province in the middle of June till the end of summer are followed by logistical distribution and in the middle of the warm year to late spring, more diverse statistical distributions are followed. The results showed that the behavior of both SPI and SPEI indicators in the monthly time intervals, especially in wet areas (Abali station), and in the 12-month period are very similar. It was also found that the two indicators did not match the annual time interval and that the same behavior of the two indicators could not be expected in the study of drought with annual data. The severity of all drought events, especially the most severe droughts, has been higher by the SPEI index for all periods of time. This is due to the sensitivity of this index to precipitation variations. Although rain has a special role in the diversity of drought time, the effect of temperature is significant and increases the phenomenon of drought. Based on the results, standardized evapotranspiration index has high accuracy in addition to having the main advantages of the SIP index, such as multi-variability and the use of minimum parameters of meteorology.

The purpose of this paper is the selection of the most suitable probability distribution function to calculate and compare the RDI and SPI drought indices. Accordingly, using the meteorological data of thirty synoptic stations in Iran, annual rainfall data series and the ratio of precipitation to potential evapotranspiration were obtained. At first, Normal or Gamma distributions and Log-normal or Gamma distributions were used to determine the SPI and RDI annual values, respectively. Then using Kolmogorov-Smirnov index, the best distribution function was obtained to fit with the data series in the studied stations. After determining the index values based on the superior distribution function and also the mentioned distribution functions, replacement of different drought classes was evaluated. The results showed that in the most stations, the mentioned distribution functions could not be selected as the most appropriate distribution function and using them in determination of the indices could change the drought classes. The results of the statistical indices (RMSER2>0.819) showed that the annual time series of the SPI and RDI indices (calculated on the basis of the most suitable probability distribution function) were approximately similar and their difference was not significant in none of the stations. Also the results showed that the RDI index was more sensitive than the SPI index to the selection of the distribution function, so the selection of the most suitable distribution function for determination of this index was more important.

Estimation of temperature probability distribution function (PDF) is a basic step for risk and uncertainty analysis in hydrology and environment studies. Most researches on temperature PDF estimation have been based on parametric approach while non-parametric approach has been considered in recent years because of some its benefit. The Ortho-Normal Series (ONS) method is a novel non-parametric method with suitable features that has recently been considered in hydrology. This method uses a number of constants with default values for its calculation, but no independent research has taken place about the importance of the default values on the precision of PDF fitting. The objective of this study is sensitivity analysis of ONS constants for precision of temperature PDF estimation which leads to a better understanding of the importance of the coefficients of this method.
First, the precision of non-parametric ONS method beside four conventional parametric methods (i.e. Gamma, Gumbel, Exponential and Log-Normal) for annual maximum and minimum temperature PDF estimation of Isfahan, Shiraz, Zahedan and Ramsar stations were investigated using Akaike Information criteria (AIC) and Mean Square Error (MSE). The non-parametric ONS method uses CJ0, CJ1, CT and CM coefficients with their default values. The reasonable domains were determined for each coefficient and a certain number of values in each domain were selected. The precision criteria corresponding to the selected value in the domains of coefficients were calculated separately. The sensitivity analysis graphs were drawn using calculated values. The CV of fitting precision criteria of each coefficient was determined considering studied data series for comparison of magnitude of sensitivity of the coefficients.
The ONS coefficients sensitivity analysis show the CT coefficient is most sensitive coefficient to changes relative to its default value. The CM and CJO coefficients have similar magnitude of sensitivity and are less sensitive to CT coefficient while CJ1 coefficient is least sensitive coefficient among all coefficients. The analysis of sensitivity analysis graph reveled that increase in precision with decrease in coefficients values and decrease in pension with increase in coefficients.
The results show sensible decrease or increase on ONS precision with changes in default values of the coefficients. Moreover it is obvious the completely acceptable precision of ONS using its default values for the coefficients but the changes in CT coefficient led to sensible improvement in precision. Therefore it can be concluded that investigation of changes in default values of ONS coefficients are an important and suitable tool to increase the precision of PDF estimation by this method.

Evaluating sampling accuracy is of great importance prior to sampling practice. Since it is expected to be a relationship between soil properties and ancillary environmental variables, proper sampling points are those that better simulate the probability distributions of these variables. The possibility of sampling from low probability tails is very low for random and regular network methods, while the Latin Hypercube Sampling (LHS) method divides the input probability distribution into equal intervals and one sample is taken from each interval. The satellite images band and digital elevation model (DEM) were used as inputs to determine the sampling points in LHS. Three methods including random, regular network and LHS sampling strategies were employed in three sampling densities of 100, 50 and 25 points in the study area of 52,000 ha to simulate the probability distribution of Landsat ETM+ bands and DEM. The simulated probability distributions were then compared with the population distribution and soil salinity data. Results indicated that there is no significant difference between the sampling strategies in 100 and 50 sampling densities to simulate the mean of population; as the sampling density decreased, the Residual Mean Square Error (RMSE) increased. In 25 point sampling density, the RMSE for LHS, regular network, and random sampling methods were 4, 7.83, and 17.5 percents, respectively. Results further indicated that LHS can efficiently simulate the input probability distribution even in low sampling densities. The RMSE values for estimating soil salinity in the original population were 4.22 and 8.66 dS/m in 100 and 25 sampling densities, respectively. Although the calculated RMSE was larger than that of input parameters of image bands and DEM, it could simulate the population probability distribution of soil salinity with enough accuracy. In conclusion, the best sampling method in this research was Latin hypercube method with a density of 25 sampling points.

Reconnaissance Drought Index (RDI) is based on fitting a Log-normal distribution to the ratio of precipitation to evapotranspiration (ETo) values in selected periods. In this index value of ETo were calculated based on mean temperature by Thorenth-Waite (Th) method. Th method، may underestimated ETo values comparing to the actual in arid and semi arid regions. The log-normal distribution may not be fitted to the ratio of precipitation to ETo values of some regions. In order to investigate the effects of these two limitations on drought situations'' changes، meteorological parameters have been used during 50 years period at 8 Synoptic Stations of Iran. In the first step، the values of RDI (Th) for any stations during the mentioned time were calculated. Then، ETo values were calculated from best fitted empirical equation in any situation of lack of parameters. Subsequently RDI (select) index were established. The Kolmogorov–Smirnov (KS) test is used to assess the goodness of fitting most appropriate distribution function to the ratio of precipitation to ETo values. Then، according to equi-probability transformation the values of RDI (Th) were modified to *RDI (Th). The occurrence of different classes of drought according to RDI (select) and/or *RDI (Th) comparing to RDI (Th) showed the elimination of any mentioned limitations may leads to changing the amount of occurrence of any drought classes in RDI (Th). Hence، The RDI (Th) modified to *RDI (select) by estimating ETo values from selected method and applying appropriate distribution function to the ratio of precipitation to ETo values.

Drought is a multivariate phenomena that caused by variation in some meteors. In this study، a new multivariable model purposed to monitor wheat drought in Mashhad and Shiraz synoptic stations during 50 years period. Purposed model was designed based on multivariable Scalogram model، with some meteorological variables as inputs such as annual evapotranspiration، number of rainy days and amounts of precipitation in autumn، winter and spring. In proposed model، imperfection of former Scalogram model including threshold levels and weights of meteorological variable were modified. In the new model drought condition will not be determined only based on precipitations amounts، but the other important meteors such as number of rainy days، evapotranspiration and especially time distribution of precipitation is considered. Results showed the modified Scalogram model، is enable to monitor agricultural drought of wheat by considering distribution of precipitation in time and the amount of evapotranspiration.

Drought duration is defined from different viewpoints. Estimation methods of drought duration return period are different in terms of drought duration definition. This paper is aimed to perform six estimation methods of drought duration return period at Kermanshah station, as a case study. The standardized precipitation index (SPI) is used to monitor drought based on historical and synthetic series of total precipitation data in annual and monthly timescales. Probability distribution of drought duration was analyzed for time series of SPI. Different methods for estimating return period of drought duration on historical and synthetic time series of SPI were applied. Findings answered two main questions: a) if the length of historical record was enough to estimate drought return period at the station of interest? b) If the obtained return periods based on different methods have enough conformity with empirically obtained return period? Results are discussed in details in this paper.