In this study, Vector Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (VAR-GARCH), copula, and copula-GARCH models were used for joint frequency analysis of storms in the ...Aras river basin in northwestern Iran in period of 1998–2018. The heteroskedasticity in the series was considered using the vector autoregressive model. Two-dimensional copulas were also used for bivariate analysis. After confirming the correlation between the pair variables of storm with one event lag (S1) and storm with no lag (S0), bivariate frequency analysis was performed. In the simulation step, the residual series of the VAR model was extracted and fitted to the GARCH model. Then, the residual series of the GARCH model was modeled using the copula model. Finally, storm with no lag (S0) affected by storm with one event lag (S1) was simulated by VAR-GARCH, copula, and copula-GARCH models. According to the coefficient of determination (
R
2
) and Nash–Sutcliffe Efficiency coefficient (NSE) and root mean square error (RMSE), the VAR-GARCH model had higher accuracy than copula and copula-GARCH models. The RMSE in the simulation of storm height using the VAR-GARCH model was estimated to be 18% and 11% less than copula and copula-GARCH models, respectively. The VAR-GARCH model provided higher accuracy in the simulations due to the consideration of different lags in the simulations and modeling the variance of the residual series. According to the Taylor diagram, the certainty of all three models in simulating storm height are acceptable. Finally, by two-dimensional analysis of pair variables of storm height and storm duration, typical curve was produced that can estimate the storm duration with different probabilities. In fact, having the storm information that has happened in the present can accurately predict the next storm information. It can be very useful in flood management and the generated curves can be used as a flood warning system in the basin.
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.
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.
AbstractIn this study, the frequency analysis of river flow deficiency (FD) of the Siminehrood River in the south of Lake Urmia located in northwest Iran was investigated with regard to rainfall ...deficiency (RD) during the period of 1992–2013 using copula functions. The main purpose of this study is to provide a comprehensive method for bivariate simulation and forecasting based on marginal distribution and joint behavior of the studied series. For this purpose, the FD and RD values were extracted using the deficiency value method. By preparing deficiency values, 57 different distribution functions were fitted to the studied values, and the generalized extreme value (GEV) distribution was selected as the best marginal distribution function based on the evaluation criteria. Before fitting the copula function, the correlation between the RD and FD values was examined using Kendall’s tau, and a correlation of 70% was obtained. After selecting the marginal distribution function and examining the correlation, the goodness of fit of seven different copula functions was examined for frequency analysis of RD and FD values in the Siminehrood River at the Dashband station. The results indicated that the Clayton copula had the best performance for creating a joint distribution of RD and FD values. It was also determined from the joint analysis of deficiency values that the FD values can be estimated with high accuracy for RD values of more than 0.68 mm. Also, the results indicated that if rainfall in the study area were less than long-term mean for 10-day and 60-day durations, with different return periods and probabilities, different conditions will occur for FD values, which can be used as typical curves for water resources management and allocation in the basin. Finally, the accuracy of the copula-based model and its conditional density in the two phases of simulation and forecasting were investigated. The accuracy of the copula-based model and its conditional density in the simulation phase was confirmed R2=0.87, root mean square error (RMSE)=0.1 m3/s, and nash-sutcliffe efficiency (NSE)=0.86. In the forecasting phase, the forecasting equation based on the proposed method had a RMSE of 0.14 m3/s and NSE of 0.89. By using the violin plot, the model certainty was also confirmed. According to the proposed equation, FD values can be forecasted affected by RD values for 10-day duration with high certainty and accuracy.
Practical ApplicationsIn this paper, a method for forecasting and simulation of meteorological and hydrological parameters is presented that considers two parameters simultaneously. This study discusses meteorology and hydrology from a different perspective. Given the current climate change, this study uses deficiency values. The proposed forecasting method provides regional results that can be used in the water resources management in each basin specifically. By implementing this method, it is easy to forecast the desired values in the basin with different probabilities and return periods. In this study, river flow deficiency (FD) affected by rainfall deficiency (RD) can be forecasted. The difference between the proposed method and other methods and models of simulation and forecasting is in the connection of two variables with each other, which makes the results more certain and reliable. This method can be used in the field of basin management and water resources allocation and also water resources monitoring.
This study investigates the performance of the M5Tree model, multivariate adaptive regression spline, least square support vector regression (LSSVR), gene expressing programming (GEP) and artificial ...neural networks methods in estimating monthly long-term rainfall. Data from 61 rain stations in Madhya Pradesh and Chhattisgarh states, Central India, were used in the applications. Geographical inputs and periodicity were used as inputs to the models, and the methods were compared with each other according to the determination coefficient (
R
2
), mean absolute errors (MAE) and root-mean-square errors (RMSE). LSSVR was found to be the best model with RMSE = 13.93 mm, MAE = 9.52 mm and
R
2
= 0.995 while the GEP provided the worst results with RMSE = 36.74 mm, MAE = 29.89 mm and
R
2
= 0.955 in prediction of long-term rainfall in the test stage. The lowest RMSE (5.53 mm) and MAE (3.89 mm) were obtained for the Rajnandgaon Station, while the Raigarh Station provided the worst accuracy (RMSE = 31.8 mm and MAE = 21.56 mm) for LSSVR model.
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.
The main goal of this research is management and comprehensive planning to optimally use the available water resources of Karde dam, using the WEAP model, and supply the demand in the agriculture and ...drinking sectors, considering the growth of their needs in the future. For this purpose, Karde Dam was first simulated in the environment of WEAP model and the model was implemented for basic conditions and seven different scenarios of development plans. According to the results obtained for the reference scenario, this dam alone does not respond to all the needs defined completely in the horizon of the project, except by applying management measures in the form of scenarios, which will reduce water consumption in different sectors of demand. Among these scenarios are demand management, increasing irrigation efficiency, using both at the same time in one scenario, changing or reducing the cultivation pattern, etc. As a result, by applying the low irrigation scenario and increasing the efficiency at the same time, it is possible to reduce the lack of water demand by 37% compared to the reference scenario, and the reservoir storage volume in this scenario increases by 25% compared to the reservoir storage volume in the reference scenario.
Multivariate probability analysis of hydrological elements using copula functions can significantly improve the modeling of complex phenomena by considering several dependent variables ...simultaneously. The main objectives of this study were to: (i) develop a stand-alone and event-based rainfall-runoff (RR) model using the common bivariate copula functions (i.e. the BCRR model); (ii) improve the structure of the developed copula-based RR model by using a trivariate version of fully-nested Archimedean copulas (i.e. the FCRR model); and (iii) compare the performance of the developed copula-based RR models in an Iranian watershed. Results showed that both of the developed models had acceptable performance. However, the FCRR model outperformed the BCRR model and provided more reliable estimations, especially for lower joint probabilities. For example, when joint probabilities were increased from 0.5 to 0.8 for the peak discharge (q
p
) variable, the reliability criteria value increased from 0.0039 to 0.8000 in the FCRR model, but only from 0.0010 to 0.6400 in the BCRR model. This is likely because the FCRR considers more than one rainfall predictor, while the BCRR considers only one.
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.
In this study, using vine copulas and tree sequences, dependence analysis of groundwater quality variables (Total hardness (TH), Sodium adsorption ratio (SAR), Sodium percentage (Na %) and magnesium ...(Mg)) was performed. For this purpose, the tree sequence of vine copulas including regular vine (R-vine), independent version of R-vine, also Gaussian version of R-vine, Gaussian independent version of R-vine, canonical vine (C-vine), independent version of C-vine, drawable vine (D-vine) and independent D-vine were evaluated independently in pairwise variables analysis. The study results of dependence structures and tree sequences of Vine copulas showed that among the studied copulas, the performance of the independent C-vine was 3.8 % better than R-vine and 0.25 % (insignificant and negligible) better than D-vine. The tree sequences provided by independent C-vine preserve correlation of pairwise variables until the last tree. In the last tree of independent C-vine, edge correlation of Mg, Na % | TH, and SAR reaches zero. Due to the proper performance of D-vine in dependence analysis of the studied variables, this copula is introduced as the selected copula.
