Metamodelling in sustainable environmental management

To evaluate decision’s sustainability, it is necessary to determine and assess the values of current and future welfare outcomes which, in turn, depend on the current and predicted status of the environment. These tasks make the application of models and mathematical tools unavoidable and justify the necessity of quantitative indicators of sustainability in decision and policy making, since environmental models are aimed to produce the results which complement observations on environmental parameters where they cannot be obtained directly. At the same time, concerns raised by the scientists and practitioners in recent years led to a suggestion that the complexity of the environmental models is one of the main obstacles in their wider use by the stakeholders. Therefore, complexity reduction is an important task for the successful application of the environmental models in the practical environmental decision-making and management. The term ‘complexity’ is used in conjunction with a computational algorithm in order to describe its efficiency during the runtime. The comparison of the complexity of any two models describing the same ecosystem must take into account the following model features: the total number of state variables included into the model, the total number of model parameters and the non-linear features of the model. It is worth noting that, in general, these three features are independent. While first two characteristics can be expressed through the complexity index, the third one cannot be easily quantified and added to the index. An obvious suggestion is that the implementation algorithms used to obtain the model solutions must also be considered in deciding on the comparative complexity of the models. In this case, the effect of non-linear terms could be taken into account, at least to some extent. Commonly used statistical approaches to building an emulator of a complex model include response surface method (RSM), neural network (NN) and kriging. In all three cases, the emulators are constructed using mathematical techniques which significantly differ from those used in the original models. This means that the emulators have sets of own parameters which do not overlap with the original model parameter sets in terms of their practical meaning or their values. Environmental models can be used in environmental management within the following settings: (1) to test possible scenarios via “what-if” analysis; (2) to find an optimal or at least satisficing scenario via optimization methods; (3) to determine key factors for a case study at hand. The replacement of an original model by an emulator looks very attractive with one reservation: it is necessary to ensure that the replacement is valid. It is obvious that in general case equal or very close values of two functions in certain points do not guarantee that their derivatives will also have close values. This means that emulators of complex environmental models can be used in the tasks which require only values of model state variables to complete the investigation. If the problem calls for optimization methods, it is necessary to ensure that the emulator contains all relevant state variables permitting to find a solution, and only non-gradient methods can be recommended to find a solutions to avoid misleading results.