A New Method for Joint Frequency Analysis of Modified Precipitation Anomaly Percentage and Streamflow Drought Index Based on the Conditional Density of Copula Functions

In this study, a new method was proposed to model the occurrence of related variables based on the conditional density of copula functions. The proposed method was adopted to investigate the dynamics of meteorological and hydrological droughts in the Zarinehroud basin, southeast of Lake Urmia, during the period 1994–2015. For this purpose, the modified precipitation anomaly percentage and streamflow drought indices were extracted. Finally, the joint frequency analysis of duration-duration and severity-severity characteristics of meteorological and hydrological droughts was analyzed. Analysis of 7 different copulas used to create the joint distribution in the Zarinehroud basin indicated that the Frank copula had the best performance in describing the relationship between the meteorological and hydrological drought severities and durations. By examining the results of the bivariate analysis of duration-duration of meteorological and hydrological droughts at different stations, the expected meteorological and hydrological drought durations were estimated in the years ahead. For example, at Chalkhmaz station, 4- to 7-month duration for the hydrological drought and 9- to 12-month duration for the meteorological drought is expected in the years ahead. The joint frequency analysis of drought characteristics allows to determine the meteorological and hydrological drought characteristics at a single station at the same time using joint probabilities. Also, the results indicated that by knowing the conditional density, the hydrological drought characteristics can be easily estimated for the given meteorological drought characteristics. This could provide users and researchers useful information about the probabilistic behavior of drought characteristics for optimal operation of surface water

Trivariate joint frequency analysis of water resources deficiency signatures using vine copulas

Investigating the interaction of water resources such as rainfall, river flow and groundwater level can be useful to know the behavior of water balance in a basin. In this study, using the rainfall, river flow and groundwater level deficiency signatures for a 60-day duration, accuracy of vine copulas was investigated by joint frequency analysis. First, while investigating correlation of pair-variables, tree sequences of C-, D- and R-vine copulas were investigated. The results were evaluated using AIC, Log likelihood and BIC statistics. Finally, according to the physics of the problem and evaluation criteria, D-vine copula was selected as the best copula and the relevant tree sequence was introduced. Kendall’s tau test was used to evaluate the correlation of pair-signatures. The results of the Kendall’s tau test showed that pair-signatures studied have a good correlation. Using D-vine copula and its conditional structure, the joint return period of groundwater deficiency signature affected by rainfall and river flow deficiency signatures was investigated. The results showed that the main changes in the groundwater level deficiency is between 0.3 and 2 m, which due to the rainfall and the corresponding river flow deficiency, return periods will be less than 5 years. Copula-based simulations were used to investigate the best copula accuracy in joint frequency analysis of the studied signatures. Using copula data of the studied signatures, the groundwater deficiency signature was simulated using D-vine copula and a selected tree sequence. The results showed acceptable accuracy of D-vine copula in simulating the copula values of the groundwater deficiency signature. After confirming the accuracy of D-vine copula, the probability of occurrence of groundwater deficiency signature was obtained from the joint probability of occurrence of other signatures. This method can be used as a general drought monitoring system for better water resources management in the basin

Multivariate analysis of rainfall and its deficiency signatures using vine copulas

In the present study, a method based on the conditional density of vine copulas was used to drought monitoring and predicting the rainfall deficiency signature for a 60-day duration in Dashband, sub-basin of Lake Urmia basin. The annual rainfall and rainfall deficiency signatures at 10-, 30- and 60-day durations were considered as variables. D-, C- and R-vine copulas were used to represent the dependence among the variables, finding that D-vine copula results to be more accurate for the case of interest. We found that, if the rainfall is less than the long-term mean in the region, the rainfall deficiency signature for near future can be estimated by acceptable accuracy. Moreover, the results of the conditional probability analysis of rainfall deficiency signature for a 60-day duration respect to the other variables showed that, on average, the probability of the occurrence of rainfall deficiency signature of 250 mm compared to the long-term mean in the study area is more than 50% per year. The results showed that the proposed approach may facilitate the meteorological drought management in the considered sub-basin