Global climate change is expected to increase both the frequency and intensity of climate extremes, such as severe drought, heat waves and periods of heavy rainfall, and there is an urgent need to understand their ecological consequences. We provide guidelines for the statistically efficient estimation of the methane emission in the sedge-grass marsh, South Bohemia, Czech Republic, developed in our recent paper. Such a study is important for a better understanding of the rate and dynamics of methane emissions from wetland ecosystems, and in particular to build a model of local methane flux. We have modeled a time series of the data via an infinite moving average process with Pareto tails of the exceedances. To assure the consistency of such an estimator, we have used both Hill and t-Hill estimators. We have provided proof of the weak consistency of the t-Hill estimator in the case of dependent data. This estimator has a simple form and it provides a nice trade-off between efficiency and robustness. Finally, we have presented a discussion on its robustness. During the talk, we will also present a model for the process of exceedences of the ebullition of methane from wetlands in the sedgegrass marsh, South Bohemia, Czech Republic by a Mixed Poisson process with mixing variable that is Pareto distributed. We investigate the properties of this process and describe it as a particular case of a counting process. We define Mixed Poisson Pareto random variable, ExponentialPareto and ErlangPareto distributions and investigate their properties. We will also show presence of the chaos of the data and the possibilities of its detection by a simple statistical technique, e.g. testing for a normality. Within this talk we will also address several methodological issues of parametric models for extremes. We will introduce a ”naturally” robust, distribution sensitive heavy tail estimator and prove its weak consistency together with its good small sample properties and some further structural properties.