Parameter estimation of copula functions using an optimization-based method

Application of the copulas can be useful for the accurate multivariate frequency analysis of hydrological phenomena. There are many copula functions and some methods were proposed for estimating the copula parameters. Since the copula functions are mathematically complicated, estimating of the copula parameter is an effortful work. In the present study, an optimization-based method (OBM) is proposed to obtain the parameters of copulas. The usefulness of the proposed method is illustrated on drought events. For this purpose, three commonly used copulas of Archimedean family, namely, Clayton, Frank, and Gumbel copulas are used to construct the joint probability distribution of drought characteristics of 60 gauging sites located in East-Azarbaijan province, Iran. The performance of OBM was compared with two conventional methods, namely, method of moments and inference function for margins. The results illustrate the supremacy of the OBM to estimate the copula parameters compared to the other considered methods.     

Comparison of the performance of power law and probability distributions in the frequency analysis of flood in Dez Basin,Iran

Determination of the return period of design flood depends on the nature of the project and the consequences of the flood and is based on economic criteria, human casualties, and hydrological factors. Underestimation of flood might result in casualties and economic damages, while the overestimation leads to capital waste. Therefore, in this research, the flood frequency analysis of Dez Basin, Iran was conducted within the period of 1956–2012 using power law approach together with ordinary distributions, including normal, log normal, Pearson type III, exponential, gamma, generalized extreme value, Nakagami, Rayleigh, logistic, generalized logistic, generalized Pareto, and Weibull distributions. The power law comes from the fractal nature of earth science phenomena such as precipitation and runoff. Accordingly, in this research the partial duration flood series of five hydrometric stations in Dez Basin were extracted using power law with the intervals of 7, 14, 30, and 60 days and then compared with the annual maxima. The results indicated that the annual maxima were not suitable for frequency analysis of the flood in Dez Basin, and the 30-day partial duration series obtained from the power law has a better correspondence with the flow and properties of the Dez Basin. The independence and stationarity of the 30-day partial duration series were examined by Wald–Wolfowitz test, confirming the independence of the considered series. Next, the power distribution and the typical statistical distributions were fitted onto the data of the flood in Dez Basin, with the performance of each distribution being investigated using normalized root-mean-square error and Nash–Sutcliffe criteria. The results revealed that in the SDZ and TPB stations, power distribution had a better performance than other considered distributions. Moreover, in the SDS, TPS, and TZ stations the power distribution stood in the second rank in terms of the best distribution. As the performance of power distribution in the estimation of the flood in Dez Basin has been very satisfactory and calculation of its parameters and its application is easier than ordinary probability distributions, thus it can be suggested as the superior distribution for flood frequency analysis in Dez Basin.     

Compositional characteristics and geodynamic significance of late Miocene volcanic rocks associated with the Chah Zard epithermal gold–silver deposit,southwest Yazd,Iran

Whole‐rock geochemical and Sr–Nd isotopic data are presented for late Miocene volcanic rocks associated with the Chah Zard epithermal Au–Ag deposit in the Urumieh‐Dokhtar Magmatic Arc (UDMA), Iran, to investigate the magma source, petrogenesis and the geodynamic evolution of the study area. The Chah Zard andesitic to rhyolitic volcanic rocks are characterized by significant Large Ion Lithophile Element (LILE) and Light Rare Earth Element (LREE) enrichment coupled with High Field Strength Element (HFSE) depletion. Our geochemical data indicate an adakitic‐like signature for the volcanic rocks (e.g. SiO₂ > 62 wt%, Al₂O₃ > 15 wt%, MgO < 1.5 wt%, Sr/Y > 70, La/Yb > 35, Yb < 1 ppm, and Y < 18 ppm, and no significant Eu anomalies), distinguishing them from the other volcanic rocks of the UDMA. The Chah Zard volcanic rocks have similar Sr and Nd isotopic compositions; the ⁸⁷Sr/⁸⁶Sr(i) ratios range from 0.704 902 to 0.705 093 and the ε_Nd(i) values are from +2.33 to +2.70. However, the rhyolite porphyry represents the final stage of magmatism in the area and has a relatively high ⁸⁷Sr/⁸⁶Sr ratio (0.705 811). Our data suggest that the andesitic magmas are from a heterogeneous source and likely to result from partial melting of a metasomatized mantle wedge associated with a mixture of subducted oceanic crust and sediment. These melts subsequently underwent fractional crystallization along with minor amounts of crustal assimilation. Our study is consistent with the model that the volcanic host rocks to epithermal gold mineralization in the UDMA are genetically related to late Miocene Neo‐Tethyan slab break‐off beneath Central Iran.     

Optimization of Gravity Concrete Dams Using the Grasshopper Algorithm (Case Study: Koyna Dam)

Geotechnical and Geological Engineering - The aim of this study is to optimize the geometric dimensions of the Koyna concrete weight dam with and without seismic forces using the grasshopper...     

Streamflow trend analysis by considering autocorrelation structure,long-term persistence,and Hurst coefficient in a semi-arid region of Iran

Due to the substantial decrease of water resources as well as the increase in demand and climate change phenomenon, analyzing the trend of hydrological parameters is of paramount importance. In the present study, investigations were carried out to identify the trends in streamflow at 20 hydrometric stations and 11 rainfall gauging stations located in Karkheh River Basin (KRB), Iran, in monthly, seasonal, and annual time scales during the last 38 years from 1974 to 2011. This study has been conducted using two versions of Mann–Kendall tests, including (i) Mann–Kendall test by considering all the significant autocorrelation structure (MK3) and (ii) Mann–Kendall test by considering LTP and Hurst coefficient (MK4). The results indicate that the KRB streamflow trend (using both test versions) has decreased in all three time scales. There is a significant decreasing trend in 78 and 73 % of the monthly cases using the MK3 and MK4 tests, respectively, while these percentages changed to 80 and 70 % on seasonal and annual time scales, respectively. Investigation of the trend line slope using Theil–Sen’s estimator showed a negative trend in all three time scales. The use of MK4 test instead of the MK3 test has caused a decrease in the significance level of Mann–Kendall Z-statistic values. The results of the precipitation trends indicate both increasing and decreasing trends. Also, the correlation between the area average streamflow and precipitation shows a strong correlation in annual time scale in the KRB.     

Spatiotemporal analysis of precipitation and temperature concentration using PCI and TCI: a case study of Khuzestan Province,Iran

Theoretical and Applied Climatology - Temperature and precipitation are the basic elements of climate, and their variation can change the water demands of different uses. In this study, the trend...     

Trend analysis of rainfall pattern over the Central India during 1901–2010

In the present study, trends of rainfall of the Central India were evaluated in monthly, seasonal, and annual time scales using the Revised Mann-Kendall (RMK) test, Sen’s slope estimator, and innovative trend method (ITM). For this purpose, the monthly rainfall data for 20 stations in Madhya Pradesh (MP) and Chhattisgarh (CG) states in Central India during 1901–2010 was used. The Sen’s slope estimator was utilized for calculating the slope of rainfall trend line. Based on the obtained results of RMK test, there is no significant trend in the stations for the January and October months. The results also showed that for MP, two out of 15 considered stations indicate significant annual trend, while the CG has four out of five stations with significant trend. The results of applying ITM test indicated that most of the stations have decreasing trends in annual (16 stations), summer (16 stations), and monsoon (11 stations) seasons, while the winter (12 stations) and post monsoon (11 stations) seasons generally show increasing trend. Unlike the RMK, the ITM shows significant increasing trend in rainfall of November and December months. The finding of current study can be used for irrigation and water resource management purpose over the Central India.     

Bivariate drought frequency analysis using the copula method

Droughts are major natural hazards with significant environmental and economic impacts. In this study, two-dimensional copulas were applied to the analysis of the meteorological drought characteristics of the Sharafkhaneh gauge station, located in the northwest of Iran. Two major drought characteristics, duration and severity, as defined by the standardized precipitation index, were abstracted from observed drought events. Since drought duration and severity exhibited a significant correlation and since they were modeled using different distributions, copulas were used to construct the joint distribution function of the drought characteristics. The parameter of copulas was estimated using the method of the Inference Function for Margins. Several copulas were tested in order to determine the best data fit. According to the error analysis and the tail dependence coefficient, the Galambos copula provided the best fit for the observed drought data. Some bivariate probabilistic properties of droughts, based on the derived copula-based joint distribution, were also investigated. These probabilistic properties can provide useful information for water resource planning and management.     

Experimental and numerical investigation for energy dissipation of supercritical flow in sudden contractions

Dealing with kinetic energy is one of the most important problems in hydraulic structures, and this energy can damage downstream structures. This study aims to study energy dissipation of supercritical water flow passing through a sudden contraction. The experiments were conducted on a sudden contraction with 15 cm width. A 30 cm wide flume was installed. The relative contraction ranged from 8.9 to 9.7, where relative contraction refers to the ratio of contraction width to initial flow depth. The Froude value in the investigation varied from 2 to 7. The contraction width of numerical simulation was 5~15 cm, the relative contraction was 8.9~12.42, and the Froude value ranged from 8.9~12.42. In order to simulate turbulence, the k-ε RNG model was harnessed. The experimental and numerical results demonstrate that the energy dissipation increases with the increase of Froude value. Also, with the sudden contraction, the rate of relative depreciation of energy is increased due to the increase in backwater profile and downstream flow depth. The experimentation verifies the numerical results with a correlation coefficient of 0.99 and the root mean square error is 0.02.