Failure Analysis of a New Irrigation Water Allocation Mode Based on Copula Approaches in the Zhanghe Irrigation District, China

The risk analysis of an irrigation water allocation strategy based on physical mechanisms is critically important in practice. Conventional risk analysis only considers the role of the channel system and ignores the factors related to on-farm ponds. This paper proposes a channel-pond joint water supply mode (CPJM) based on copula approaches. Two copulas, the Plackett copula and No.16 copula, are chosen and two types of analyses are carried out with the proposed mode: (1) a risk assessment of CPJM with joint probability and conditional probability; and (2) determination of the water supply strategy given the pond water supply frequency. With a case study of the second channel in the Zhanghe Irrigation District (ZID), Southern China, nine combinations of channel water supply frequency (CWSF) and pond water supply frequency (PWSF) are studied. The results reveal that the failure probabilities of the joint distribution and the conditional distribution of the CPJM are 0.02%–16.54% and 0.45%–33.08%, respectively, with corresponding return period of 42–5000 and 10–222 years. Nevertheless, a previous study has shown that the real probability is 33.3%, which means that the return period is equals to three years. Therefore, the objective failure evaluation of the irrigation water-use strategy is useful for water saving in this channel system. Moreover, the irrigation water allocation strategy can be determined and the failure charts relating the CWSF and PWSF can be obtained for a predetermined PWSF. Thus, the channel-pond joint water supply mode provides a more reasonable estimate of the irrigation water allocation strategy reliability.