Toward an estimation of the relationship between cyclonic structures and damages at the ground in Europe

Cyclonic systems dominate European and Mediterranean meteorology throughout the year and often induce severe weather in terms of heavy and/or long-lasting precipitation with related phenomena such as strong winds and lightning. Surface cyclonic structures are often related to well defined precipitation patterns with different scales, duration and intensity. Cyclones confined in the upper troposphere, usually referred to as cut off low, may induce instability at lower levels and the development of convective precipitation. In this work the occurrence of cyclonic events (discriminated between surface ones and cut-off lows) is analyzed and matched with an economic losses database to highlight a relation between the atmospheric structures and the impact on the social environment in terms of casualties and material damages. The study focus on the continental Europe and, based on the ERA-40 reanalysis, two databases of surface cyclones and cut-off lows have been constructed by means of automatic pattern recognition algorithms. The impact on the local communities is estimated from an insurance company record, which provides the location, date and type of the events, as well as related losses in terms of damages and casualties. Results show the relatively high impact of cyclonic structures on human life in Europe: most of the weather induced damages occur close to a cyclonic center, especially during warm months. Damages and human losses are more frequent from late summer to January, and precipitation is the most relevant meteorological damaging feature throughout the year

Asymptotic forecast uncertainty and the unstable subspace in the presence of additive model error

It is well understood that dynamic instability is among the primary drivers of forecast uncertainty in chaotic, physical systems. Data assimilation techniques have been designed to exploit this phenomenon, reducing the effective dimension of the data assimilation problem to the directions of rapidly growing errors. Recent mathematical work has, moreover, provided formal proofs of the central hypothesis of the assimilation in the unstable subspace methodology of Anna Trevisan and her collaborators: for filters and smoothers in perfect, linear, Gaussian models, the distribution of forecast errors asymptotically conforms to the unstable-neutral subspace. Specifically, the column span of the forecast and posterior error covariances asymptotically align with the span of backward Lyapunov vectors with nonnegative exponents. Earlier mathematical studies have focused on perfect models, and this current work now explores the relationship between dynamical instability, the precision of observations, and the evolution of forecast error in linear models with additive model error. We prove bounds for the asymptotic uncertainty, explicitly relating the rate of dynamical expansion, model precision, and observational accuracy. Formalizing this relationship, we provide a novel, necessary criterion for the boundedness of forecast errors. Furthermore, we numerically explore the relationship between observational design, dynamical instability, and filter boundedness. Additionally, we include a detailed introduction to the multiplicative ergodic theorem and to the theory and construction of Lyapunov vectors. While forecast error in the stable subspace may not generically vanish, we show that even without filtering, uncertainty remains uniformly bounded due its dynamical dissipation. However, the continuous reinjection of uncertainty from model errors may be excited by transient instabilities in the stable modes of high variance, rendering forecast uncertainty impractically large. In the context of ensemble data assimilation, this requires rectifying the rank of the ensemble-based gain to account for the growth of uncertainty beyond the unstable and neutral subspace, additionally correcting stable modes with frequent occurrences of positive local Lyapunov exponents that excite model errors

Model error and sequential data assimilation. A deterministic formulation

Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modeled on the basis of simple assumptions such as bias, white noise, first order Markov process. In the present work, a formulation of the sequential extended Kalman filter is proposed, based on recent findings on the universal deterministic behavior of model errors in deep contrast with previous approaches (Nicolis, 2004). This new scheme is applied in the context of a spatially distributed system proposed by Lorenz (1996). It is found that (i) for short times, the estimation error is accurately approximated by an evolution law in which the variance of the model error (assumed to be a deterministic process) evolves according to a quadratic law, in agreement with the theory. Moreover, the correlation with the initial condition error appears to play a secondary role in the short time dynamics of the estimation error covariance. (ii) The deterministic description of the model error evolution, incorporated into the classical extended Kalman filter equations, reveals that substantial improvements of the filter accuracy can be gained as compared with the classical white noise assumption. The universal, short time, quadratic law for the evolution of the model error covariance matrix seems very promising for modeling estimation error dynamics in sequential data assimilation

Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error

The ensemble Kalman filter and its variants have shown to be robust for data assimilation in high dimensional geophysical models, with localization, using ensembles of extremely small size relative to the model dimension. However, a reduced rank representation of the estimated covariance leaves a large dimensional complementary subspace unfiltered. Utilizing the dynamical properties of the filtration for the backward Lyapunov vectors, this paper explores a previously unexplained mechanism, providing a novel theoretical interpretation for the role of covariance inflation in ensemble-based Kalman filters. Our derivation of the forecast error evolution describes the dynamic upwelling of the unfiltered error from outside of the span of the anomalies into the filtered subspace. Analytical results for linear systems explicitly describe the mechanism for the upwelling, and the associated recursive Riccati equation for the forecast error, while nonlinear approximations are explored numerically

The Cemetery and the Fear of the Dead

Fear is a characteristic feature of many legends. And the fear of the death is probably our deepest fear. Death is a crucial event in folk culture, as it triggers an existential crisis which must be duly managed. The living need to distance themselves from the dead in order not to lose their own “presence” in the world. To maintain this distance, people can rely on a dedicated place, the cemetery, where the fear of the dead can be mastered and framed in a sacred dimension. Cemetery may be regarded as a liminal, hybrid space, connecting life and death, the human and the divine, the visible and the invisible. Hence, it can turn into a critical, dangerous place, a “legend landscape”, where odd, mysterious, frightening encounters are possible or, at least, believable. This is especially so if one enters a cemetery at night, when it is forbidden to the living and the darkness creates the perfect stage for fearsome presences. In the ATU 1676B narrative type, an individual bets to enter a cemetery at night in order to show her/his courage and/or refute the belief of the dead as ghosts, but this gamble results in a death from fright. A different case concerns the fate of those who face the night in the cemetery with genuine courage and respect towards the dead, as in a folktale collected by W.B. Yeats (ATU 326), and a (true) story of a woman sleeping in the cemetery (Motif Index C735.2.5). Overall, the cemetery emerges as an ideal setting for a cautionary tale, through which local communities meditate on key issues such as death, fear and belief/non-belief

Linking the anomaly initialization approach to the mapping paradigm: a proof-of-concept study

Seasonal-to-decadal predictions are initialized using observations of the present climatic state in full field initialization (FFI). Such model integrations undergo a drift toward the model attractor due to model deficiencies that incur a bias in the model. The anomaly initialization (AI) approach reduces the drift by adding an estimate of the bias onto the observations at the expense of a larger initial error. In this study FFI is associated with the fidelity paradigm, and AI is associated with an instance of the mapping paradigm, in which the initial conditions are mapped onto the imperfect model attractor by adding a fixed error term; the mapped state on the model attractor should correspond to the nature state. Two diagnosis tools assess how well AI conforms to its own paradigm under various circumstances of model error: the degree of approximation of the model attractor is measured by calculating the overlap of the AI initial conditions PDF with the model PDF; and the sensitivity to random error in the initial conditions reveals how well the selected initial conditions on the model attractor correspond to the nature states. As a useful reference, the initial conditions of FFI are subjected to the same analysis. Conducting hindcast experiments using a hierarchy of low-order coupled climate models, it is shown that the initial conditions generated using AI approximate the model attractor only under certain conditions: differences in higher-than-first-order moments between the model and nature PDFs must be negligible. Where such conditions fail, FFI is likely to perform better

Controlling instabilities along a 3DVar analysis cycle by assimilating in the unstable subspace: a comparison with the EnKF

A hybrid scheme obtained by combining 3DVar with the Assimilation in the Unstable Subspace (3DVar-AUS) is tested in a QG model, under perfect model conditions, with a fixed observational network, with and without observational noise. The AUS scheme, originally formulated to assimilate adaptive observations, is used here to assimilate the fixed observations that are found in the region of local maxima of BDAS vectors (Bred vectors subject to assimilation), while the remaining observations are assimilated by 3DVar. The performance of the hybrid scheme is compared with that of 3DVar and of an EnKF. The improvement gained by 3DVar-AUS and the EnKF with respect to 3DVar alone is similar in the present model and observational configuration, while 3DVar-AUS outperforms the EnKF during the forecast stage. The 3DVar-AUS algorithm is easy to implement and the results obtained in the idealized conditions of this study encourage further investigation toward an implementation in more realistic contexts

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

Impact of rheology on probabilistic forecasts of sea ice trajectories: application for search and rescue operations in the Arctic

We present a sensitivity analysis and discuss the probabilistic forecast capabilities of the novel sea ice model neXtSIM used in hindcast mode. The study pertains to the response of the model to the uncertainty on winds using probabilistic forecasts of ice trajectories. neXtSIM is a continuous Lagrangian numerical model that uses an elasto-brittle rheology to simulate the ice response to external forces. The sensitivity analysis is based on a Monte Carlo sampling of 12 members. The response of the model to the uncertainties is evaluated in terms of simulated ice drift distances from their initial positions, and from the mean position of the ensemble, over the mid-term forecast horizon of 10 days. The simulated ice drift is decomposed into advective and diffusive parts that are characterised separately both spatially and temporally and compared to what is obtained with a free-drift model, that is, when the ice rheology does not play any role in the modelled physics of the ice. The seasonal variability of the model sensitivity is presented and shows the role of the ice compactness and rheology in the ice drift response at both local and regional scales in the Arctic. Indeed, the ice drift simulated by neXtSIM in summer is close to the one obtained with the free-drift model, while the more compact and solid ice pack shows a significantly different mechanical and drift behaviour in winter. For the winter period analysed in this study, we also show that, in contrast to the free-drift model, neXtSIM reproduces the sea ice Lagrangian diffusion regimes as found from observed trajectories. The forecast capability of neXtSIM is also evaluated using a large set of real buoy's trajectories and compared to the capability of the free-drift model. We found that neXtSIM performs significantly better in simulating sea ice drift, both in terms of forecast error and as a tool to assist search and rescue operations, although the sources of uncertainties assumed for the present experiment are not sufficient for complete coverage of the observed IABP positions

Developing a dynamically based assimilation method for targeted and standard observations

International audienceIn a recent study, a new method for assimilating observations has been proposed and applied to a small size nonlinear model. The assimilation is obtained by confining the analysis increment in the unstable subspace of the Observation-Analysis-Forecast (OAF) cycle system, in order to systematically eliminate the dynamically unstable components, present in the forecast error, which are responsible for error growth. Based on the same ideas, applications to more complex models and different, standard and adaptive, observation networks are in progress. Observing System Simulation Experiments (OSSE), performed with an atmospheric quasi-geostrophic model, with a restricted "land" area where vertical profiles are systematically observed, and a wider "ocean" area where a single supplementary observation is taken at each analysis time, are reviewed. The adaptive observation is assimilated either with the proposed method or, for comparison, with a 3-D VAR scheme. The performance of the dynamic assimilation is very good: a reduction of the error of almost an order of magnitude is obtained in the data void region. The same method is applied to a primitive equation ocean model, where "satellite altimetry" observations are assimilated. In this standard observational configuration, preliminary results show a less spectacular but significant improvement obtained by the introduction of the dynamical assimilation