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  1. Viscous shocks are a particular type of extreme event in nonlinear multiscale systems, and their representation requires small scales. Model reduction can thus play an essential role in reducing the computational cost for the prediction of shocks. Yet, reduced models typically aim to approximate large-scale dominating dynamics, which do not resolve the small scales by design. To resolve this representation barrier, we introduce a new qualitative characterization of the space–time locations of shocks, named the “shock trace,” via a space–time indicator function based on an empirical resolution-adaptive threshold. Unlike exact shocks, the shock traces can be captured within the representationmore »capacity of the large scales, thus facilitating the forecast of the timing and locations of the shocks utilizing reduced models. Within the context of a viscous stochastic Burgers equation, we show that a data-driven reduced model, in the form of nonlinear autoregression (NAR) time series models, can accurately predict the random shock traces, with relatively low rates of false predictions. Furthermore, the NAR model, which includes nonlinear closure terms to approximate the feedback from the small scales, significantly outperforms the corresponding Galerkin truncated model in the scenario of either noiseless or noisy observations. The results illustrate the importance of the data-driven closure terms in the NAR model, which account for the effects of the unresolved dynamics brought by nonlinear interactions.« less
    Free, publicly-accessible full text available April 4, 2023
  2. Fisher, E. ; Boyd, E. ; Brondizio, E. (Ed.)
    If the success of agricultural intensification continues to rely on the depletion of aquifers and exploitation of (female) labour, transformations to groundwater sustainability will be impossible to achieve. Hence, the development of new groundwater imaginaries, based on alternative ways of organizing society-water relations is highly important. This paper argues that a comparative documentation of grass-roots initiatives to care for, share or recharge aquifers in places with acute resource pressures provides an important source of inspiration. Using a grounded anti-colonial and feminist approach, we combine an ethnographic documentation of groundwater practices with hydrogeological and engineering insights to enunciate, normatively assess andmore »jointly learn from the knowledges, technologies and institutions that characterize such initiatives. Doing this usefully shifts the focus of planned efforts to regulate and govern groundwater away from government efforts to control individual pumping behaviours, to the identification of possibilities to anchor transformations to sustainability in collective action.« less