This paper proposes a model-free nonparametric estimator of conditional quantile of a time-series regression model where the covariate vector is repeated many times for different values of the response. This type of data abounds in climate studies. Although the use of quantile regression is standard in such studies, the opportunity to improve the results using the replicated nature of data is increasingly realized. The proposed method exploits this feature of the data and improves on the restrictive linear model structure of conventional quantile regression. Relevant asymptotic theories for the nonparametric estimators of the mean and variance function of the model are derived under a very general framework. We conduct a detailed simulation study that demonstrates the gain in efficiency of the proposed method over other benchmark models, especially when the actual data-generating process entails a nonlinear mean function and heteroskedastic pattern with time-dependent covariates. The predictive accuracy of the nonparametric method is remarkably high compared to other approaches when attention is on the higher quantiles of the variable of interest. The usefulness of the proposed method is then illustrated with two climatological applications, one with a well-known tropical cyclone wind-speed data and the other with an air pollution data.