Faculty Publications

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Bivariate Modeling of Hydroclimatic Variables in Humid Tropical Coastal Region Using Archimedean Copulas
(American Society of Civil Engineers (ASCE) onlinejls@asce.org 1801 Alexander Bell DriveGEO Reston VA 20191 Alabama, 2020) Uttarwar, S.B.; Deb Barma, S.; Mahesha, M.
The present study focuses on the dependence modeling of hydroclimatic variables such as the El Niño-Southern Oscillation (ENSO) index, precipitation, tidal height, and groundwater level (GWL) in humid tropical coastal region of India. The rank-based correlation coefficient was used to determine the dependence between the pairs of cumulative monsoon precipitation of June-July-August-September (P_JJAS) and the postmonsoon groundwater level (PMGWL), ENSO-P_JJAS, ENSO-PMGWL, and GWL-tidal height. The results indicated that P_JJAS-PMGWL, ENSO-PMGWL, and GWL-tidal height had significant dependence, whereas P_JJAS-ENSO had no significant dependence. The best fit distributions for P_JJAS, PMGWL, and tidal height were found to be lognormal, extreme value, and generalized extreme value distributions, respectively, whereas for the ENSO index, it was the normal kernel-density function. The Archimedean families of copulas were used for dependence modeling, and it was observed that the ENSO-PMGWL was best modeled by the Frank copula, the P_JJAS-PMGWL by the Gumbel-Hougaard copula, and the GWL-tidal height by the Frank copula. The copula-based conditional probability for the Gumbel-Hougaard and Frank copulas for GWL were obtained to understand the risk associated with other hydroclimatic variables. Thus, copula-based dependence modeling could be useful for understanding the risk among hydroclimatic variables including groundwater. © 2020 American Society of Civil Engineers.
Bivariate Drought Characterization of Two Contrasting Climatic Regions in India Using Copula
(American Society of Civil Engineers (ASCE), 2021) Sajeev, A.; Deb Barma, S.; Mahesha, A.; Shiau, J.-T.
This study aims to construct the multiple time-scale joint distributions of drought duration and severity using two-dimensional copulas and compare the drought characteristics in India's two contrasting climate regions: the arid Rajasthan and humid, tropical Kerala. The drought occurrences were defined by the standardized precipitation index (SPI) with a threshold below -0.8 at time scales of 3, 6, 12, and 24 months for 1900-2016. Significant correlations were noted between the drought severity and drought duration in both regions. The Clayton copula gave a better fit than other copulas for modeling the dependence among the observed drought duration and severity. The results indicate that the probability of short-term droughts (SPI-3 and SPI-6) is more significant than those of long-term droughts (SPI-12 and SPI-24) for an identical drought event in both regions. Also, the probability of severe drought events with greater duration and severity for long-term droughts (SPI-12 and SPI-24) is higher in Kerala than that in western Rajasthan. For all the time-scale SPIs, the conditional probability of drought severity for a given duration exceeding a threshold showed an increasing trend in both regions. Furthermore, the conditional probability of the drought duration given the severity for short-term droughts is greater than that of the long-term droughts for the same drought event. For short-term droughts, the conditional return period of an identical drought event is lower in Kerala than in western Rajasthan. In contrast, the conditional return period of long-term droughts is lower in western Rajasthan. Additionally, copula-based nonexceedance conditional distributions for the major crops were established based on rainfall. © 2020 American Society of Civil Engineers.
Copula-Based Frequency and Coincidence Risk Analysis of Floods in Tropical-Seasonal Rivers
(American Society of Civil Engineers (ASCE), 2021) Muthuvel, D.; Mahesha, A.
The conventional method of univariate flood frequency analysis based solely on peak flow (Q) overlooks the influence of other characteristic flood variables, such as the accumulated volume (V) of the flood and the duration (D) of flood events. A copula-based multivariate model that represents the joint behavior of these dependent flood variables could aid in computing joint return periods of flood events in tropical, seasonal rivers of India. In connection with the potential locations of high flood risk among west-flowing rivers, multivariate flood frequency analysis was performed on the Bharatapuzha, Periyar, and Chaliyar Rivers of the state of Kerala, India. A comparison of univariate return periods with multivariate return periods reveals that the intersection of flood variables corresponding to a 20-year univariate return period yields a trivariate return period of 91 years at Bharatapuzha and 144 years at Periyar and Chaliyar. The return period by the union of such flood variables is 10 years. The choice of flood variables and their combination depend on the problem at hand. Additionally, basinwise confluence flood frequency models are built with the peak flow at each stream as the random variables show their spatial interdependencies using conditional probabilities and return periods. The copula-based flood coincidence risk model captures the temporal aspect of the co-occurrence of flood peaks in a basin's streams. The co-occurrence of annual flood peaks between the stream pairs of the Bharatapuzha, Periyar, and Muvathapuzha basins is the highest toward the end of July with probabilities of approximately 2.2×10-4 (at the Kumbidi and Mankara stations), 3×10-4, and 1×10-3, respectively. A trio of copula-based multivariate flood frequency, confluence flood frequency, and flood coincidence risk models could be used to design safe and economic hydrologic infrastructure. © 2021 American Society of Civil Engineers.

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