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Model uncertainty quantification is an essential component of effective data assimilation. Model errors associated with sub-grid scale processes are often represented through stochastic parameterizations of the unresolved process. Many existing Stochastic Parameterization schemes are only applicable when knowledge of the true sub-grid scale process or full observations of the coarse scale process are available, which is typically not the case in real applications. We present a methodology for estimating the statistics of sub-grid scale processes for the more realistic case that only partial observations of the coarse scale process are available. Model error realizations are estimated over a training period by minimizing their conditional sum of squared deviations given some informative covariates (e.g., state of the system), constrained by available observations and assuming that the observation errors are smaller than the model errors. From these realizations a conditional probability distribution of additive model errors given these covariates is obtained, allowing for complex non-Gaussian error structures. Random draws from this density are then used in actual ensemble data assimilation experiments. We demonstrate the efficacy of the approach through numerical experiments with the multi-scale Lorenz 96 system using both small and large time scale separations between slow (coarse scale) and fast (fine scale) variables. The resulting error estimates and forecasts obtained with this new method are superior to those from two existing methods.
The fluxes of water and solutes in the subsurface compartment of the Critical Zone are temporally dynamic and it is unclear how this impacts microbial mediated nutrient cycling in the spatially heterogeneous subsurface. To investigate this, we undertook numerical modeling, simulating the transport in a wide range of spatially heterogeneous domains, and the biogeochemical transformation of organic carbon and nitrogen compounds using a complex microbial community with four (4) distinct functional groups, in water saturated subsurface compartments. We performed a comprehensive uncertainty analysis accounting for varying residence times and spatial heterogeneity. While the aggregated removal of chemical species in the domains over the entire simulation period was approximately the same as that in steady state conditions, the sub-scale temporal variation of microbial biomass and chemical discharge from a domain depended strongly on the interplay of spatial heterogeneity and temporal dynamics of the forcing. We showed that the travel time and the Damkohler number (Da) can be used to predict the temporally varying chemical discharge from a spatially heterogeneous domain. In homogeneous domains, chemical discharge in temporally dynamic conditions could be double of that in the steady state conditions while microbial biomass varied up to 75% of that in steady state conditions. In heterogeneous domains, the interquartile range of uncertainty in chemical discharge in reaction dominated systems (log(10)Da > 0) was double of that in steady state conditions. However, high heterogeneous domains resulted in outliers where chemical discharge could be as high as 10-20 times of that in steady state conditions in high flow periods. And in transport dominated systems (log(10)Da < 0), the chemical discharge could be half of that in steady state conditions in unusually low flow conditions. In conclusion, ignoring spatio-temporal heterogeneities in a numerical modeling approach may exacerbate inaccurate estimation of nutrient export and microbial biomass. The results are relevant to long-term field monitoring studies, and for homogeneous soil column-scale experiments investigating the role of temporal dynamics on microbial redox dynamics.
In-depth understanding of the potential implications of climate change is required to guide decision- and policy-makers when developing adaptation strategies and designing infrastructure suitable for future conditions. Impact models that translate potential future climate conditions into variables of interest are needed to create the causal connection between a changing climate and its impact for different sectors. Recent surveys suggest that the primary strategy for validating such models (and hence for justifying their use) heavily relies on assessing the accuracy of model simulations by comparing them against historical observations. We argue that such a comparison is necessary and valuable, but not sufficient to achieve a comprehensive evaluation of climate change impact models. We believe that a complementary, largely observation-independent, step of model evaluation is needed to ensure more transparency of model behavior and greater robustness of scenario-based analyses. This step should address the following four questions: (1) Do modeled dominant process controls match our system perception? (2) Is my model's sensitivity to changing forcing as expected? (3) Do modeled decision levers show adequate influence? (4) Can we attribute uncertainty sources throughout the projection horizon? We believe that global sensitivity analysis, with its ability to investigate a model's response to joint variations of multiple inputs in a structured way, offers a coherent approach to address all four questions comprehensively. Such additional model evaluation would strengthen stakeholder confidence in model projections and, therefore, into the adaptation strategies derived with the help of impact models. This article is categorized under: Climate Models and Modeling > Knowledge Generation with Models Assessing Impacts of Climate Change > Evaluating Future Impacts of Climate Change