Estimating model evidence using data assimilation

We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the discrimination between a factual model–which corresponds, to the best of the modeller's knowledge, to the situation in the actual world in which a sequence of events has occurred–and a counterfactual model, in which a particular forcing or process might be absent or just quantitatively different from the actual world. Three different ensemble‐DA methods are reviewed for this purpose: the ensemble Kalman filter (EnKF), the ensemble four‐dimensional variational smoother (En‐4D‐Var), and the iterative ensemble Kalman smoother (IEnKS). An original contextual formulation of model evidence (CME) is introduced. It is shown how to apply these three methods to compute CME, using the approximated time‐dependent probability distribution functions (pdfs) each of them provide in the process of state estimation. The theoretical formulae so derived are applied to two simplified nonlinear and chaotic models: (i) the Lorenz three‐variable convection model (L63), and (ii) the Lorenz 40‐variable midlatitude atmospheric dynamics model (L95). The numerical results of these three DA‐based methods and those of an integration based on importance sampling are compared. It is found that better CME estimates are obtained by using DA, and the IEnKS method appears to be best among the DA methods. Differences among the performance of the three DA‐based methods are discussed as a function of model properties. Finally, the methodology is implemented for parameter estimation and for event attribution

Full-field and anomaly initialization using a low-order climate model: a comparison and proposals for advanced formulations

Initialization techniques for seasonal-to-decadal climate predictions fall into two main categories; namely full-field initialization (FFI) and anomaly initialization (AI). In the FFI case the initial model state is replaced by the best possible available estimate of the real state. By doing so the initial error is efficiently reduced but, due to the unavoidable presence of model deficiencies, once the model is let free to run a prediction, its trajectory drifts away from the observations no matter how small the initial error is. This problem is partly overcome with AI where the aim is to forecast future anomalies by assimilating observed anomalies on an estimate of the model climate. The large variety of experimental setups, models and observational networks adopted worldwide make it difficult to draw firm conclusions on the respective advantages and drawbacks of FFI and AI, or to identify distinctive lines for improvement. The lack of a unified mathematical framework adds an additional difficulty toward the design of adequate initialization strategies that fit the desired forecast horizon, observational network and model at hand. Here we compare FFI and AI using a low-order climate model of nine ordinary differential equations and use the notation and concepts of data assimilation theory to highlight their error scaling properties. This analysis suggests better performances using FFI when a good observational network is available and reveals the direct relation of its skill with the observational accuracy. The skill of AI appears, however, mostly related to the model quality and clear increases of skill can only be expected in coincidence with model upgrades. We have compared FFI and AI in experiments in which either the full system or the atmosphere and ocean were independently initialized. In the former case FFI shows better and longer-lasting improvements, with skillful predictions until month 30. In the initialization of single compartments, the best performance is obtained when the stabler component of the model (the ocean) is initialized, but with FFI it is possible to have some predictive skill even when the most unstable compartment (the extratropical atmosphere) is observed. Two advanced formulations, least-square initialization (LSI) and exploring parameter uncertainty (EPU), are introduced. Using LSI the initialization makes use of model statistics to propagate information from observation locations to the entire model domain. Numerical results show that LSI improves the performance of FFI in all the situations when only a portion of the system's state is observed. EPU is an online drift correction method in which the drift caused by the parametric error is estimated using a short-time evolution law and is then removed during the forecast run. Its implementation in conjunction with FFI allows us to improve the prediction skill within the first forecast year. Finally, the application of these results in the context of realistic climate models is discussed

Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models

Recent progress in machine learning has shown how to forecast and, to some extent, learn the dynamics of a model from its output, resorting in particular to neural networks and deep learning techniques. We will show how the same goal can be directly achieved using data assimilation techniques without leveraging on machine learning software libraries, with a view to high-dimensional models. The dynamics of a model are learned from its observation and an ordinary differential equation (ODE) representation of this model is inferred using a recursive nonlinear regression. Because the method is embedded in a Bayesian data assimilation framework, it can learn from partial and noisy observations of a state trajectory of the physical model. Moreover, a space-wise local representation of the ODE system is introduced and is key to coping with high-dimensional models. It has recently been suggested that neural network architectures could be interpreted as dynamical systems. Reciprocally, we show that our ODE representations are reminiscent of deep learning architectures. Furthermore, numerical analysis considerations of stability shed light on the assets and limitations of the method. The method is illustrated on several chaotic discrete and continuous models of various dimensions, with or without noisy observations, with the goal of identifying or improving the model dynamics, building a surrogate or reduced model, or producing forecasts solely from observations of the physical model

DADA: data assimilation for the detection and attribution of weather and climate-related events

A new nudging method for data assimilation, delay‐coordinate nudging, is presented. Delay‐coordinate nudging makes explicit use of present and past observations in the formulation of the forcing driving the model evolution at each time step. Numerical experiments with a low‐order chaotic system show that the new method systematically outperforms standard nudging in different model and observational scenarios, also when using an unoptimized formulation of the delay‐nudging coefficients. A connection between the optimal delay and the dominant Lyapunov exponent of the dynamics is found based on heuristic arguments and is confirmed by the numerical results, providing a guideline for the practical implementation of the algorithm. Delay‐coordinate nudging preserves the easiness of implementation, the intuitive functioning and the reduced computational cost of the standard nudging, making it a potential alternative especially in the field of seasonal‐to‐decadal predictions with large Earth system models that limit the use of more sophisticated data assimilation procedures

Rank deficiency of Kalman error covariance matrices in linear time-varying system with deterministic evolution

We prove that for-linear, discrete, time-varying, deterministic system (perfect-model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance matrices to be less than or equal to the number of nonnegative Lyapunov exponents of the system. Further, the support of these error covariance matrices is shown to be confined to the space spanned by the unstable-neutral backward Lyapunov vectors, providing the theoretical justification for the methodology of the algorithms that perform assimilation only in the unstable-neutral subspace. The equivalent property of the autonomous system is investigated as a special case

Deep learning subgrid-scale parametrisations for short-term forecasting of sea-ice dynamics with a Maxwell elasto-brittle rheology

We introduce a proof of concept to parametrise the unresolved subgrid scale of sea-ice dynamics with deep learning techniques. Instead of parametrising single processes, a single neural network is trained to correct all model variables at the same time. This data-driven approach is applied to a regional sea-ice model that accounts exclusively for dynamical processes with a Maxwell elasto-brittle rheology. Driven by an external wind forcing in a 40 km×200 km domain, the model generates examples of sharp transitions between unfractured and fully fractured sea ice. To correct such examples, we propose a convolutional U-Net architecture which extracts features at multiple scales. We test this approach in twin experiments: the neural network learns to correct forecasts from low-resolution simulations towards high-resolution simulations for a lead time of about 10 min. At this lead time, our approach reduces the forecast errors by more than 75 %, averaged over all model variables. As the most important predictors, we identify the dynamics of the model variables. Furthermore, the neural network extracts localised and directional-dependent features, which point towards the shortcomings of the low-resolution simulations. Applied to correct the forecasts every 10 min, the neural network is run together with the sea-ice model. This improves the short-term forecasts up to an hour. These results consequently show that neural networks can correct model errors from the subgrid scale for sea-ice dynamics. We therefore see this study as an important first step towards hybrid modelling to forecast sea-ice dynamics on an hourly to daily timescale.</p

LCA assessment related to the evolution of the earthquake performance of a strategic structure

Several buildings and infrastructures, located in urban areas, are identified as strategic in the case of an earthquake event. This is the case of a water treatment plant which is currently built in Genoa, Italy, and which has been assessed for the scope of this research. Since the structure has been designed following the seismic design prescriptions, this work aims to provide a preliminary assessment of how the degradation mechanisms do affect its earthquake response. To this purpose, both chloride attack and carbonation are taken into account as main degradation mechanisms. Moreover, due to the importance of the water treatment plant, to develop a realistic Life Cycle Assessment (LCA) analysis, the earthquake resistance of the structure and its evolution over time as a function of the aforesaid degradation mechanisms, have been accounted as Serviceability Limit State to estimate the frequency of the maintenance activities needed in a timeframe of 100 years

Machine learning for earth system observation and prediction

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Melatonin treatment in patients with burning mouth syndrome: A triple-blind, placebo-controlled, crossover randomized clinical trial

Aims: To evaluate the efficacy of melatonin compared to placebo in reducing pain associated with burning mouth syndrome (BMS), as well as side effects of treatment and effects on sleep quality, anxiety, and serum and salivary melatonin levels. Methods: In this triple-blind, randomized clinical trial, 20 BMS patients (mean age \ub1 standard deviation: 64.4 \ub1 11.5 years; range: 35 to 82 years) were enrolled to receive melatonin (12 mg/day) or placebo for 8 weeks in a crossover design. After treatment, changes in pain from baseline were ascertained by patient self-assessment with a verbal category scale and a visual analog scale. Secondary outcomes included evaluation of changes in sleep quality and anxiety. Data were subjected to analysis of variance (ANOVA), Fisher exact test, paired t test, Wilcoxon signed rank test, or chi-square test, as appropriate. Results: Melatonin was not superior to placebo in reducing pain. Melatonin significantly improved anxiety scores, though without strong clinical relevance. Independent of treatment, sleep quality did not significantly change during the trial, although melatonin slightly increased the number of hours slept. After active treatment, the mean \ub1 standard error serum melatonin level peaked at 1,520 \ub1 646 pg/mL. A generally safe pharmacologic profile of melatonin was observed, and the placebo and melatonin treatments resulted in similar adverse effects. Conclusion: Within the limitations of this study, melatonin did not exhibit higher efficacy than placebo in relieving pain in BMS patients

Lichen Planus and hepatitis C virus : a multicentre study of patients with oral lesions and systematic review

BACKGROUND: An association between hepatitis C virus (HCV) infection and lichen planus (LP) has been investigated, but results have been inconsistent. OBJECTIVES: To investigate the relationship between LP and HCV seropositivity. Methods In a cross-sectional study we tested the sera of 303 consecutive newly diagnosed patients with histologically proven LP referred to three Italian centres for the presence of anti-HCV IgG. A comparable control group was also tested. Next, in a systematic review, studies were identified by searching different databases in April 2004. Inclusion criteria were: (i) analytical study design; (ii) clinical and histological diagnosis of LP; and (iii) serological test for anti-HCV antibodies as main outcome. The risk of bias was assessed on the basis of characteristics of the study group, appropriateness of the control group and study design. Pooled data were analysed by calculating odds ratios (ORs), using a random effects model. RESULTS: In the cross-sectional study, nearly one in five (19.1%) of the LP group was HCV positive, while a much lower prevalence of infection was found in the control group (3.2%) [OR 7.08; 95% confidence interval (CI) 3.43-14.58]. The systematic review yielded 25 relevant studies, six of which had a low risk of bias. There was a statistically significant difference in the proportion of HCV-seropositive subjects among patients with LP, compared with controls (OR 4.80; 95% CI 3.25-7.09). Following subgroup analyses, the variability of HCV prevalence in patients with LP seemed to depend on geographical area, but not on age. CONCLUSIONS: Anti-HCV circulating antibodies are more common in patients with LP than in controls, although such an association may not be significant in some geographical areas