Trend analysis of rainfall time series for Sindh river basin in India

The main goal of this paper is to estimate a set of optimal seasonal, daily, and hourly values of atmospheric turbidity and surface radiative parameters Ångström’s turbidity coefficient (β), Ångström’s wavelength exponent (α), aerosol single scattering albedo (ω_o), forward scatterance (F_c) and average surface albedo (ρ_g), using the Brute Force multidimensional minimization method to minimize the difference between measured and simulated solar irradiance components, expressed as cost functions. In order to simulate the components of short-wave solar irradiance (direct, diffuse and global) for clear sky conditions, incidents on a horizontal surface in the Metropolitan Area of Rio de Janeiro (MARJ), Brazil (22° 51′ 27″ S, 43° 13′ 58″ W), we use two parameterized broadband solar irradiance models, called CPCR2 and Iqbal C, based on synoptic information. The meteorological variables such as precipitable water (u_w) and ozone concentration (u_o) required by the broadband solar models were obtained from moderate-resolution imaging spectroradiometer (MODIS) sensor on Terra and Aqua NASA platforms. For the implementation and validation processes, we use global and diffuse solar irradiance data measured by the radiometric platform of LabMiM, located in the north area of the MARJ. The data were measured between the years 2010 and 2012 at 1-min intervals. The performance of solar irradiance models using optimal parameters was evaluated with several quantitative statistical indicators and a subset of measured solar irradiance data. Some daily results for Ångström’s wavelength exponent α were compared with Ångström’s parameter (440–870 nm) values obtained by aerosol robotic network (AERONET) for 11 days, showing an acceptable level of agreement. Results for Ångström’s turbidity coefficient β, associated with the amount of aerosols in the atmosphere, show a seasonal pattern according with increased precipitation during summer months (December–February) in the MARJ.     

Regional bivariate modeling of droughts using L-comoments and copulas

The regional bivariate modeling of drought characteristics using the copulas provides valuable information for water resources management and drought risk assessment. The regional frequency analysis (RFA) can specify the similar sites within a region using L-comoments approach. One of the important steps in the RFA is estimating regional parameters of the copula function. In the present study, an optimization-based method along with the adjusted charged system search are introduced and applied to estimate the regional parameters of the copula models. The capability of the proposed methodology is illustrated by copula functions on drought events. Three commonly used copulas containing Clayton, Frank and Gumbel are employed to derive the joint distribution of drought severity and duration. The result of the new method are compared to the method of moments and after applying several goodness-of-fit tests, the results indicate that the new method provides higher accuracy than the classic one. Furthermore, the results of the upper tail dependence coefficient indicate that the Gumbel copula is the best-fitted copula among the other ones for modeling drought characteristics.     

Prediction of Groundwater Level in Ardebil Plain Using Support Vector Regression and M5 Tree Model

The Ardebil plain, which is located in northwest Iran, has been faced with a recent and severe decline in groundwater level caused by a decrease of precipitation, successive long‐term droughts, and overexploitation of groundwater for irrigating the farmlands. Predictions of groundwater levels can help planners to deal with persistent water deficiencies. In this study, the support vector regression (SVR) and M5 decision tree models were used to predict the groundwater level in Ardebil plain. The monthly groundwater level data from 24 piezometers for a 17‐year period (1997 to 2013) were used for training and test of models. The model inputs included the groundwater levels of previous months, the volume of entering precipitation into every cell, and the discharge of wells. The model output was the groundwater level in the current month. In order to evaluate the performance of models, the correlation coefficient (R) and the root‐mean‐square error criteria were used. The results indicated that both SVR and M5 decision tree models performed well for the prediction of groundwater level in the Ardebil plain. However, the results obtained from the M5 decision tree model are more straightforward, more easily applied, and simpler to interpret than those from the SVR. The highest accuracy was obtained using the SVR model to predict the groundwater level from the Ghareh Hasanloo and Khalifeloo piezometers with R = 0.996 and R = 0.983, respectively.     

Bivariate frequency analysis of low flow using copula functions (case study: Dez River Basin,Iran)

Accurate estimation of low flow as a criterion for different objectives in water resource management, including drought is of crucial importance. Despite the complex nature of water deficits, univariate methods have often been used to analyze the frequency of low flows. In this study, low flows of Dez River basin were examined during period of 1956–2012 using copula functions at the upstream of headbranches’ junction. For this purpose, at first 7-day series of low flow was extracted at the studied stations, then their homogeneity was examined by Mann–Kendall test. The results indicated that 7-day low flow series of Dez basin were homogenous. In the next stage, 12 different distribution functions were fitted onto the low flow data. Finally, for Sepid Dasht Sezar (SDS), Sepid Dasht Zaz (SDZ), and Tang Panj Bakhtiyari (TPB) stations, logistic distribution had the best fit, while for Tang Panj Sezar (TPS) station, GEV distribution enjoyed the best fit. After specifying the best fitted marginal distributions, seven different copula functions including Ali–Mikhail–Haq (AMH), Frank, Clayton, Galambos, Farlie–Gumbel–Morgenstern (FGM), Gumbel–Hougaard (GH), and Plackett were used for bivariate frequency analysis of the 7-day low flow series. The results revealed that the GH copula had the best fitness on paired data of SDS and SDZ stations. For TPS and TPB stations, Frank copula has had the best correspondence with empirical copula values. Next, joint and conditional return periods were calculated for the low flow series at the upstream of branches’ junction. The results of this study indicated that the risk of incidence of severe drought is higher in upstream stations (SDZ and SDS) when compared with downstream stations (TPB and TPS) in Dez basin. Generally, application of multivariate analysis allows researchers to investigate hydrological events with a more comprehensive view by considering the simultaneous effect of the influencing factors on the phenomenon of interest. It also enables them to evaluate different combinations of required scenarios for integrated management of basin and planning to cope with the damages caused by natural phenomena.     

Investigation of spatial and temporal variability of precipitation in Iran over the last half century

Investigation of the precipitation phenomenon as one of the most important meteorological factors directly affecting access to water resources is of paramount importance. In this study, the precipitation concentration index (PCI) was calculated using annual precipitation data from 34 synoptic stations of Iran over a 50-year period (1961–2010). The trend of precipitation and the PCI index were analyzed using the Mann–Kendall test after removing the effect of autocorrelation coefficients in annual and seasonal time scales. The results of zoning the studied index at annual time scale revealed that precipitation concentration follows a similar trend within two 25-year subscales. Furthermore, the PCI index in central and southern regions of the country, including the stations of Kerman, Bandarabbas, Yazd, Zahedan, Shahrekord, Birjand, Bushehr, Ahwaz, and Esfahan indicates a strong irregularity and high concentration in atmospheric precipitations. In annual time scale, none of the studied stations, had shown regular concentration (PCI < 10). Analyzing the trend of PCI index during the period of 1961–2010 witnessed an insignificant increasing (decreasing) trend in 16 (15) stations for winter season, respectively, while it faced a significant negative trend in Dezful, Saghez, and Hamedan stations. Similarly, in spring, Kerman and Ramsar stations exhibited a significant increasing trend in the PCI index, implying significant development of precipitation concentration irregularities in these two stations. In summer, Gorgan station showed a strong and significant irregularity for the PCI index and in autumn, Tabriz and Zahedan (Babolsar) stations experienced a significant increasing (decreasing) trend in the PCI index. At the annual time scale, 50 % of stations experienced an increasing trend in the PCI index. Investigating the changes in the precipitation trend also revealed that in annual time scale, about 58 % of the stations had a decreasing trend. In winter, which is the rainiest season in Iran, about 64 % of stations experienced a decreasing trend in precipitation that caused an increasing trend in PCI index. Comparing the spatial distribution of PCI index within two 25 years sub-periods indicated that the PCI index of the second sub-period increased in the spring time scale that means irregularity of precipitation distribution has been increased. But in the other seasons any significant variations were not observed. Also in the annual time scale the PCI index increased in the second sub-period because of the increasing trend of precipitation.     

Modeling flood event characteristics using D-vine structures

The authors investigate the use of drawable (D-)vine structures to model the dependences existing among the main characteristics of a flood event, i.e., flood volume, flood peak, duration, and peak time. Firstly, different three- and four-dimensional probability distributions were built considering all the permutations of the conditioning variables. The Frank copula was used to model the dependence of each pair of variables. Then, the appropriate D-vine structures were selected using information criteria and a goodness-of-fit test. The influence of varying the data length on the selected D-vine structure was also investigated. Finally, flood event characteristics were simulated using the four-dimensional D-vine structure.     

Spatio-temporal analysis of daily,seasonal and annual precipitation concentration in Jharkhand state,India

Nowadays, climate change and global warming have led to changes in the distribution of precipitation, which affect on the availability of water resources. Therefore, investigating the temporal and spatial variations of precipitation in the previous period is highly important in the future planning for flood control and local management of water resources. Considering the importance of this issue, in the present study, the precipitation concentration indices have been used for analysing precipitation changes at daily, seasonal, and annual time scales in the period of 1971 to 2011 over the Jharkhand state, India. Also, Modified Mann–Kendall test has used to study the trend of precipitation concentration indices in annual and seasonal time scales. The result shows a highly irregular and non-uniform distribution in the annual scale. For the seasonal scale an irregular and non-uniform distribution has been also observed, although the summer had a better situation than other seasons. For daily scale, none of the stations had a regular concentration and in the northeast and southern parts of the study area, there have been more irregularities. Furthermore, the results of investigating annual precipitation trend showed a combination of increasing and decreasing trend over the study area. The results of this study can be applied to manage water supplies, drainage projects, construct collection structures of urban flood, develop plans to prevent soil erosion, and designing appropriate plans to cope with drought conditions.     

Ground water quality classification by decision tree method in Ardebil region,Iran

A decision tree-based approach is proposed to predict ground water quality based on the United States Salinity Laboratory (USSL) diagram using the data from aquifers in agricultural lands of Ardebil province, northwest of Iran. Several combinations of hydro chemical parameters of groundwater and monthly precipitation with different lag time were considered to find an accurate and economical alternative for groundwater quality classification. The performance evaluation was based on the number of correctly classified instances (CCI) and kappa statistics. The results suggested the suitability of decision tree-based classification approach for the used data sets. The overall average of CCI and kappa statistic for the prediction of groundwater quality classes based on the USSL diagram was 0.88 and 0.83 %, respectively. Principal component analysis (PCA) was also used to determine the important parameters for groundwater quality classification. The results showed that groundwater quality classification by decision tree is more precise and efficient in comparison with PCA. The best alternative could evaluate groundwater quality class with only two parameters: electrical conductivity and cumulative precipitation of 11 months earlier. The developed model is able to predict water quality class by only two variables and this lead to a reduction in the number of variables analyzed on a routine basis, resulting in a significant reduction in laboratory costs and latency times between the sampling moment and the outcome of the laboratory analyses.     

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.     

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.