Probabilistic prediction of hydroclimatic variables with nonparametric quantification of uncertainty

A semiparametric, copula-based approach is proposed to capture the dependence between teleconnected hydroclimatic variables for the prediction of response variable using the information of climate precursors. The copulas have an excellent property to study the scale-free dependence structure while preserving such dependence during simulation. This property is utilized in the proposed approach. The usefulness of the proposed method can be recognized in three distinct aspects: (1) It captures the dependence pattern preserving scale-free or rank-based "measure of association'' between the variables. (2) The proposed method is able to quantify the uncertainty associated with the relationship between teleconnected variables due to various factors; thus, the probabilistic predictions are available along with information of uncertainty. (3) Instead of parametric probability distribution, nonparametrically estimated probability densities for data sets can be handled by the proposed approach. Thus, the proposed method can be applied to capture the relationship between teleconnected hydroclimatic variables having some linear and/ or nonlinear cause-effect relationship. The proposed method is illustrated by an example of the most discussed problem of Indian summer monsoon rainfall (ISMR) and two different large-scale climate precursors, namely, El Nino Southern Oscillation (ENSO) and Equatorial Indian Ocean Oscillation (EQUINOO). The dependence between them is captured and investigated for its potential use to predict the monthly variation of ISMR using the proposed method. Predicted rainfall is shown to correspond well with the observed rainfall with a correlation coefficient of 0.81 for the summer monsoon months, i.e., June through September. Moreover, the uncertainty associated with the predicted values is also made available through boxplots. The method, being general, can be applied to similar analysis to assess the dependence between teleconnected hydroclimatic variables for other regions of the world and for different temporal scales such as seasonal.