Multivariate Copula-Based Joint Probability Distribution of Water Supply and Demand in Irrigation District

Based on the data series of rainfall, reference crop evapotranspiration and irrigation water from 1970 to 2013 in the Luhun irrigation district of China, the multivariate joint probability of water supply and demand are constructed with student t-copula function. The results show that student t-copula function can indicate the associated dependence structure amongst these variables well, and the constructed multivariate copula-based joint probability distribution reveal the statistical characteristics and occurrence probability of different combinations of water supply and water demand. Moreover, the trivariate joint probability distribution is more reasonable than the bivariate distribution to reflect the water shortage risk, and these joint distribution values of different combinations of water supply and demand can provide the technological support for water shortage risk evaluation in the irrigation district.

[1]  Guohe Huang,et al.  A Factorial-based Dynamic Analysis Method for Reservoir Operation Under Fuzzy-stochastic Uncertainties , 2013, Water Resources Management.

[2]  Vijay P. Singh,et al.  Bivariate rainfall frequency distributions using Archimedean copulas , 2007 .

[3]  L. S. Pereira,et al.  Stochastic Prediction of Drought Class Transitions , 2008 .

[4]  Yingying Chen,et al.  Spatio-temporal variation of reference evapotranspiration and aridity index in the Loess Plateau Region of China, during 1961-2012 , 2014 .

[5]  Use of observed scaled daily storm profiles in a copula based rainfall disaggregation model , 2012 .

[6]  Peter F. Rasmussen,et al.  Bivariate frequency analysis: discussion of some useful concepts in hydrological application , 2002 .

[7]  W. Horwath,et al.  The role of irrigation runoff and winter rainfall on dissolved organic carbon loads in an agricultural watershed , 2013 .

[8]  Mike Spiliotis,et al.  Drought Severity Assessment Based on Bivariate Probability Analysis , 2011 .

[9]  C. Michele,et al.  Multivariate real-time assessment of droughts via copula-based multi-site Hazard Trajectories and Fans , 2015 .

[10]  Guohe Huang,et al.  Hydrologic risk analysis in the Yangtze River basin through coupling Gaussian mixtures into copulas , 2016 .

[11]  N. Guttman.  COMPARING THE PALMER DROUGHT INDEX AND THE STANDARDIZED PRECIPITATION INDEX 1 , 1998 .

[12]  D. Khalili,et al.  Factors Influencing Markov Chains Predictability Characteristics, Utilizing SPI, RDI, EDI and SPEI Drought Indices in Different Climatic Zones , 2013, Water Resources Management.

[13]  Francesco Serinaldi,et al.  Asymmetric copula in multivariate flood frequency analysis , 2006 .

[14]  Fateh Chebana,et al.  On the prediction of extreme flood quantiles at ungauged locations with spatial copula , 2016 .

[15]  Nicolas R. Dalezios,et al.  Severity-duration-frequency analysis of droughts and wet periods in Greece , 2000 .

[16]  Abdul Aziz Jemain,et al.  IDF relationships using bivariate copula for storm events in Peninsular Malaysia , 2012 .

[17]  Martine van der Ploeg,et al.  Short-term rainfall forecasts as a soft adaptation to climate change in irrigation management in North-East India , 2013 .

[18]  Sheng Yue,et al.  Applying Bivariate Normal Distribution to Flood Frequency Analysis , 1999 .

[19]  Jenq-Tzong Shiau,et al.  Fitting Drought Duration and Severity with Two-Dimensional Copulas , 2006 .

[20]  C. Genest,et al.  Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask , 2007 .

[21]  Luis S. Pereira,et al.  Prediction of SPI Drought Class Transitions Using Markov Chains , 2007 .

[22]  Alberto Lamberti,et al.  Coastal flooding: A copula based approach for estimating the joint probability of water levels and waves , 2015 .

[23]  Davar Khalili,et al.  Utilization of Time-Based Meteorological Droughts to Investigate Occurrence of Streamflow Droughts , 2010 .

[24]  W. Xiao,et al.  Study on Markov Joint Transition Probability and Encounter Probability of Rainfall and Reference Crop Evapotranspiration in the Irrigation District , 2014, Water Resources Management.

[25]  Satish Chandra,et al.  Multivariate modeling of flood flows , 1998 .

[26]  Guangtao Fu,et al.  Copula-based frequency analysis of overflow and flooding in urban drainage systems , 2014 .

[27]  D. Yan,et al.  Assessing the impact of climatic factors on potential evapotranspiration in droughts in North China , 2014 .

[28]  Xiangyu Xu,et al.  Copula based drought frequency analysis considering the spatio-temporal variability in Southwest China , 2015 .

[29]  Yang Hong,et al.  Uncertainty analysis of bias from satellite rainfall estimates using copula method , 2014 .

[30]  M. Sklar.  Fonctions de repartition a n dimensions et leurs marges , 1959 .

[31]  Andrew W. Western,et al.  Forecasting daily reference evapotranspiration for Australia using numerical weather prediction outputs , 2014 .

[32]  Rao S. Govindaraju,et al.  A copula-based joint deficit index for droughts. , 2010 .

[33]  R. S. Kurothe,et al.  Derived flood frequency distribution for negatively correlated rainfall intensity and duration , 1997 .

[34]  L. S. Pereira,et al.  Modeling malt barley water use and evapotranspiration partitioning in two contrasting rainfall years. Assessing AquaCrop and SIMDualKc models , 2015 .

[35]  G. Zhao,et al.  Distinguishing the impacts of human activities and climate variability on runoff and sediment load change based on paired periods with similar weather conditions: A case in the Yan River, China , 2015 .

[36]  C. Genest,et al.  A semiparametric estimation procedure of dependence parameters in multivariate families of distributions , 1995 .

[37]  L. Kazembe,et al.  Linking rainfall and irrigation to clinically reported malaria cases in some villages in Chikhwawa district, Malawi , 2011 .

[38]  Sheng Yue,et al.  Joint probability distribution of annual maximum storm peaks and amounts as represented by daily rainfalls , 2000 .

[39]  Chong-yu Xu,et al.  Analysis and prediction of reference evapotranspiration with climate change in Xiangjiang River Basin, China , 2015 .

[40]  Shaoming Pan,et al.  Influence of climate change on reference evapotranspiration and aridity index and their temporal-spatial variations in the Yellow River Basin, China, from 1961 to 2012 , 2015 .

[41]  B. Breckling,et al.  Modelling regional variability of irrigation requirements due to climate change in Northern Germany. , 2016, The Science of the total environment.